ORDER

An administrative law judge denied Rocco DeGrazio’s application for supplemental security income, finding that he was not disabled. The Appeals Council upheld the decision, despite new medical evidence that was unavailable to the ALJ. DeGrazio sought judicial review, and the district court ordered a remand to the agency so that the ALJ could evaluate the new medical evidence. DeGrazio, who opposed the Commissioner’s motion on the ground that the existing record shows him to be disabled, has appealed to this court and argues that the district court (acting through a magistrate judge by consent) should instead have instructed the Commissioner to award benefits. We conclude that the district court exceeded its statutory authority; we therefore vacate the court’s order and remand for further proceedings.

DeGrazio’s application for benefits was precipitated by two surgeries in December 2011 to repair a hemorrhage and a vascular anomaly in his brain. He asserts that the residual effects of those surgeries— including headaches, fatigue, weakness, chronic back pain, and balance problems— prevent him from working. The ALJ concluded, however, that DeGrazio (who had worked as a roofer before the surgeries) retains the ability to perform “light work” as a housekeeper, machine feeder, or production worker and, thus, is not disabled.

DeGrazio filed an administrative appeal and submitted as new evidence an audiom-etric evaluation — conducted a month after the ALJ’s decision — which confirms that he has substantial hearing loss. The agency’s regulations require the Appeals Council to consider “new and material evidence” when deciding whether an ALJ’s decision qualifies for review. 20 C.F.R. §§ 404.970(b), 416.1470(b); Farrell v. Astrue, 692 F.3d 767, 771 (7th Cir. 2012). The Appeals Council denied review with the explanation that it had “considered ... the additional evidence” and “found that this information does not provide a basis for changing the Administrative Law Judge’s decision.” Although the wording of this explanation might give the impression that the Appeals Council did consider the au-diometric evaluation, we previously have recognized that this language is boilerplate and actually means that the Appeals Council decided that the evidence is not “new and material” and, thus, did not consider it. See Farrell, 692 F.3d at 771.

In the district court the Commissioner did not file an answer to DeGrazio’s complaint or otherwise defend the agency’s decision. Instead, on the day that the Commissioner’s memorandum in support of that decision was due, the agency’s lawyer moved for a 30-day extension of time on the ground that unspecified “issues in the case” required “further consultation with the client Agency, so as to determine how to best proceed in this case.” The district court granted the extension, and the Commissioner then moved to reverse and remand under sentence four of 42 U.S.C. § 405(g). A sentence-four remand “depends on a finding of error in the Commissioner’s decision,” Perlman v. Swiss Bank Corp. Comprehensive Disability Prot. Plan, 195 F.3d 975, 978 (7th Cir. *6511999), but the Commissioner identified no error justifying reversal, instead asserting that remand was necessary so that the agency could consider the audiometric evaluation, which the Commissioner characterized as “new evidence.” The Commissioner did not acknowledge that the audiometric evaluation had been presented to the Appeals Council, or that the Appeals Council had concluded that the evidence was not “new and material.” Submitted with the Commissioner’s motion was a proposed order that incorrectly describes the motion as a “Joint Motion for Remand” and which, in contrast with the text of the motion, does not mention reversing the agency’s denial of benefits.

The district court, which was misled by the Commissioner’s representation that DeGrazio joined in the request for a remand, entered an order similar to the one proposed by the Commissioner, stating that the case was being remanded to the Commissioner “pursuant to Sentence Four” of § 405(g) but saying nothing about affirming, modifying, or reversing the agency’s decision. DeGrazio sought reconsideration of this remand order, arguing that the district court should have reversed the agency’s decision and instructed the Commissioner to award benefits rather than acquiescing to what, in his view, is a needless remand. The court rejected DeGrazio’s argument, but now quoted not sentence four but sentence six of § 405(g), which authorizes a remand where the Commissioner “requests a remand before answering the complaint, or where new, material evidence is adduced that was for good cause not presented before the agency.” Shalala v. Schaefer, 509 U.S. 292, 297 n. 2, 113 S.Ct. 2625, 125 L.Ed.2d 239 (1993). There was good cause for remand, the court asserted, because the agency had not had the opportunity to evaluate the “new evidence” of DeGrazio’s hearing loss.

On appeal to this court, DeGrazio still maintains that the district court erred by not instructing the agency to immediately award benefits. The Commissioner counters that a remand under sentence four of § 405(g) is appropriate because the ALJ should evaluate the evidence of De-Grazio’s hearing loss. But we are not convinced that the Commissioner’s request for a remand satisfied the requirements of § 405(g).

Section 405(g) gives district courts only limited authority to remand cases to the agency; “remand orders must either accompany a final judgment affirming, modifying, or reversing the administrative decision in accordance with sentence four, or conform with the requirements outlined by Congress in sentence six.” Melkonyan v. Sullivan, 501 U.S. 89, 101-02, 111 S.Ct. 2157, 115 L.Ed.2d 78 (1991). The Commissioner requested, and the district court purported to enter, a remand under sentence four. But the court’s order does not comply with the statutory requirements of sentence four because that order does not affirm, modify, or reverse the Commissioner’s decision. See Melkonyan, 501 U.S. at 98, 111 S.Ct. 2157; Perlman, 195 F.3d at 978; Young v. Sullivan, 972 F.2d 830, 833-34 (7th Cir. 1992); Raitport v. Callahan, 183 F.3d 101, 104-05 (2d Cir. 1999). Because the court bypassed a substantive evaluation of the agency’s denial of benefits, a remand was not authorized — and is not sustainable — under sentence four of § 405(g).

In denying DeGrazio’s request for reconsideration, the district court did quote sentence six, so we have considered the possibility that the court changed course and remanded under that sentence instead of sentence four. Remand orders under sentence six are interlocutory and cannot be appealed by the claimant. See *652Melkonyan, 501 U.S. at 101-02, 111 S.Ct. 2157; Chowdhury v. Ashcroft, 241 F.3d 848, 852 (7th Cir. 2001); Krishnan v. Barnhart, 328 F.3d 685, 691 (D.C.Cir. 2003); but cf. Travis v. Sullivan, 985 F.2d 919, 920-23 (7th Cir. 1993) (concluding that Commissioner may appeal sentence-six remand if the order would be “effectively unreviewable after a resolution of the merits of the litigation.”). Sentence six authorizes a district court to remand without ruling on the merits in two circumstances: when (1) the Commissioner requests a remand before filing her answer and demonstrates good cause, or (2) there is evidence that is new and material, plus a showing of “good cause for the failure to incorporate such evidence into the record in a prior proceeding.” 42 U.S.C. § 405(g). But neither of those circumstances is present in this case. The evidence that the Commissioner characterized as “new” in her motion — the audiometric report that confirmed DeGrazio’s hearing loss — was not new for purposes of sentence six because it already had been presented to the Appeals Council. See Sullivan v. Finkelstein, 496 U.S. 617, 626, 110 S.Ct. 2658, 110 L.Ed.2d 563 (1990) (explaining that a remand under sentence six is “appropriate when the district court learns of evidence not in existence or available to the claimant at the time of the administrative proceeding”); Ingram v. Comm’r of Soc. Sec. Admin., 496 F.3d 1253, 1269 (11th Cir. 2007) (concluding that, under sentence six, a district court cannot remand for evaluation of evidence that was previously submitted to Appeals Council). For that reason, the district court’s determination that allowing the agency to evaluate this “new” evidence provided “good cause” for remand rests on an assertion by the Commissioner that is simply inaccurate. Because the Commissioner did not identify new evidence or articulate good cause warranting remand, the district court could not have ordered a remand under sentence six.

The court’s order thus fails to satisfy the requirements of either sentence four or sentence six, and since § 405(g) does not authorize remands on any other basis, we are compelled to vacate the order and return this case to the district court for further proceedings. See Melkonyan, 501 U.S. at 102, 111 S.Ct. 2157; Raitport, 183 F.3d at 105. The Commissioner — apparently anticipating this outcome — asks that we instead conduct our own merits review of the ALJ’s decision and declare the denial of benefits to be correct. Yet in the district court, the Commissioner never defended the ALJ’s decision and, in fact, asserted that “defense of this case is not warranted” because the audiometric evaluation could affect the disability determination. We often remind claimants who neglected to raise an argument in the district court that they cannot raise that argument for the first time on appeal. See Skarbek v. Barnhart, 390 F.3d 500, 505 (7th Cir. 2004); Schoenfeld v. Apfel, 237 F.3d 788, 793 (7th Cir. 2001). We see no reason why the Commissioner should not be held to the same standard here, given that she presented the district court with no argument on the merits and instead asked the district court only for reversal and remand.

By arguing that the evidence of DeGra-zio’s hearing loss warrants a remand, the Commissioner has conceded that the Appeals Council made a prejudicial legal error in deeming this evidence not to be “new and material.” Accordingly, the district court should, at a minimum, enter a judgment reversing the agency’s decision on this ground and remanding to the agency so that it may evaluate the effect of this evidence on DeGrazio’s claim. Of course, before taking that step, the court must conduct a full merits review to determine *653whether the agency committed other errors which would compel additional relief.

The district court’s order is VACATED, and the case is REMANDED to that court for further proceedings consistent with this order. DeGrazio’s pending motions— requesting appointment of counsel, oral argument, and other unspecified relief — are DENIED.