
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 $\mathbf{u}$ and $\mathbf{v}$ be unit vectors, such that $\mathbf{u} \cdot \mathbf{v} = 0$. Let $\mathbf{w} = \mathbf{u} \times \mathbf{v} + 2\mathbf{u}$. Compute the value of $\mathbf{u} \cdot (\mathbf{v} \times \mathbf{w})$.

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