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 15th day of March, 2021.

                                        /s/ Arlene Morris
                                        ---------------------------
                                        Arlene Morris