
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
Let \(\mathbf{A}\) and \(\mathbf{B}\) be matrices such that
\[
\mathbf{A} + \mathbf{B} = \mathbf{A} \mathbf{B}.
\]
If \(\mathbf{A} \mathbf{B} = \begin{pmatrix} 5 & 2 \\ -3 & 9 \end{pmatrix},\) find \(\mathbf{B} \mathbf{A}.\)

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