Including GPL external library in MIT code

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I am shipping software licensed under the MIT license.

Under the application tree, I have also a file that is part of the software. Inside of this file there are the exact contents of an external library, licensed under GPL. There is also other code (by me), licensed under the MIT license. The section of this file that contains the library is left intact and the library is not altered.

Can I release my software under the MIT license? Should I include the GPL license (I'm quite sure the answer is yes)? Should I also include a README with indications such as "the part of the file X is licensed under the GPL license as it is an external library, the rest is MIT"?

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