
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 $\mathbf{A}$ be a matrix, and let $\mathbf{u}$ and $\mathbf{x}$ be vectors, such that
\[
\mathbf{A} \mathbf{u} = \begin{pmatrix} 3 \\ -7 \end{pmatrix} \quad \text{and} \quad \mathbf{A} \mathbf{x} = \begin{pmatrix} -2 \\ 5 \end{pmatrix}.
\]
Compute $\mathbf{A} (3 \mathbf{u} - 2 \mathbf{x})$.

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