
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
Given that $\mathbf{u}, \mathbf{v},$ and $\mathbf{w}$ are unit vectors, find the maximum value of
\[
\|\mathbf{u} - \mathbf{v}\|^2 + \|\mathbf{u} - \mathbf{w}\|^2 + \|\mathbf{v} - \mathbf{w}\|^2 + \|\mathbf{u} + \mathbf{v} + \mathbf{w}\|^2.
\]

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