
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 vectors $\mathbf{u}$, $\mathbf{v}$, and $\mathbf{w}$ be such that $\|\mathbf{u}\| = 4$, $\|\mathbf{v}\| = 5$, and $\|\mathbf{w}\| = 7$. Furthermore, assume $\mathbf{u} \cdot \mathbf{v} = 0$ and $\mathbf{u} + \mathbf{v} + \mathbf{w} = \mathbf{0}$. Compute $\mathbf{u} \cdot \mathbf{w} + \mathbf{v} \cdot \mathbf{w}$.

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