
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 $\mathbf{p} = \begin{pmatrix} 2 \\ -1 \\ 1 \end{pmatrix}$ and $\mathbf{q} = \begin{pmatrix} -1 \\ 3 \\ 2 \end{pmatrix}$. Find the vector $\mathbf{u}$ that satisfies $\mathbf{u} \times \mathbf{p} = \mathbf{q} \times \mathbf{p}$ and $\mathbf{u} \times \mathbf{q} = \mathbf{p} \times \mathbf{q}$.

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