
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 \(\mathbf{u}, \mathbf{v}, \mathbf{w}\) be vectors such that \(\|\mathbf{u}\| = \|\mathbf{v}\| = 2\) and \(\|\mathbf{w}\| = 3.\) Find the maximum value of
\[
\|\mathbf{u} - 3\mathbf{v}\|^2 + \|\mathbf{v} - 3\mathbf{w}\|^2 + \|\mathbf{w} - 3\mathbf{u}\|^2.
\]

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