
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 $\mathbf{X} \mathbf{Y} = \begin{pmatrix} 25/4 & 5/4 \\ -10/4 & 10/4 \end{pmatrix},$ find $\mathbf{Y} \mathbf{X}.$

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