
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 $\mathbf{u}, \mathbf{v}$ be unit vectors, and let $\mathbf{w}$ be a vector such that $2(\mathbf{u} \times \mathbf{v}) + \mathbf{u} = 3\mathbf{w}$ and $3(\mathbf{w} \times \mathbf{u}) = 2\mathbf{v}$. Compute $\mathbf{u} \cdot (\mathbf{v} \times \mathbf{w})$.

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