
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 \(\mathbf{X}\) and \(\mathbf{Y}\) be matrices such that
\[ \mathbf{X} + \mathbf{Y} = \mathbf{X} \mathbf{Y}. \]
If \(\mathbf{X} \mathbf{Y} = \begin{pmatrix} 16/3 & 2 \\ -10/3 & 10/3 \end{pmatrix},\) find \(\mathbf{Y} \mathbf{X}.\)

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