POWER OF ATTORNEY

     Know all by these presents that the undersigned hereby constitutes and
appoints each of Ryan Murr and Robert Phillips, and any of their substitutes,
signing singly, as the undersigned's true and lawful attorney-in-fact to:

     1.   prepare, execute in the undersigned's name and on the undersigned's
          behalf, and submit to the U.S. Securities and Exchange Commission (the
          "SEC") a Form ID, including amendments thereto, and any other document
          necessary or appropriate to obtain codes, passwords, and passphrases
          enabling the undersigned to make electronic filings with the SEC of
          reports require by the Securities Exchange Act of 1934 or any rule or
          regulation of the SEC;

     2.   execute for and on behalf of the undersigned, in the undersigned's
          capacity as a director and/or officer of Cogent Biosciences Inc. (the
          "Company"), Forms 3, 4, and 5 in accordance with Section 16(a) of the
          Securities Exchange Act of 1934 and the rules thereunder;

     3.   do and perform any and all acts for and on behalf of the
          undersigned which may be necessary or desirable to complete and
          execute any such Form 3, 4, or 5, complete and execute any amendment
          or amendments thereto, and timely file such form with the SEC and any
          securities exchange or similar authority; and

     4.   take any other action of any type whatsoever in connection with
          the foregoing which, in the opinion of such attorney-in-fact, may be
          of benefit to, in the best interest of, or legally required by, the
          undersigned, it being understood that the documents executed by such
          attorney-in-fact on behalf of the undersigned pursuant to this Power
          of Attorney shall be in such form and shall contain such terms and
          conditions as such attorney-in-fact may approve in such attorney-in-
          fact's discretion.

     The undersigned hereby grants to each such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that each such attorney-in-fact, or such
attorney-in-fact's substitute or substitutes, shall lawfully do or cause to be
done by virtue of this power of attorney and the rights and powers herein
granted.  The undersigned also ratifies hereby any action previously taken by
each attorney-in-fact that would have been authorized by this power of attorney
if it has been in effect at the time such action was taken.  The undersigned
acknowledges that each attorney-in-fact, in serving in such capacity at the
request of the undersigned, is not assuming, nor is the Company assuming, any of
the undersigned's responsibilities to comply with Section 16 of the Securities
Exchange Act of 1934, as amended.

     This Power of Attorney shall remain in full force and effect until the
earliest to occur of (a) undersigned is no longer required to file Forms 3, 4,
and 5 with respect to the undersigned's holdings of and transactions in
securities issued by the Company, (b) revocation by the undersigned in a signed
writing delivered to the foregoing attorneys-in-fact or (c) as to any attorney-
in-fact individually, until such attorney-in-fact is no longer employed by the
Company or its subsidiaries.

IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this 24th day of February, 2021.


                                                 /s/ Todd Shegog
                                                 ----------------------
                                                 Todd Shegog