
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Find the matrix $\mathbf{M}$ that rotates the columns of a $3 \times 3$ matrix to the right. In other words, 
\[
\mathbf{M} \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} = \begin{pmatrix} c & a & b \\ f & d & e \\ i & g & h \end{pmatrix}.
\]
If no such matrix $\mathbf{M}$ exists, then enter the zero matrix.

Present the answer in LaTex format: \boxed{Your answer}
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