
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 \(\mathbf{x}, \mathbf{y},\) and \(\mathbf{z}\) be vectors such that \(\|\mathbf{x}\| = 2\), \(\|\mathbf{y}\| = 1\), and \(\|\mathbf{z}\| = 3\). Find the maximum value of
\[
\|\mathbf{x} - 3\mathbf{y}\|^2 + \|\mathbf{y} - 3\mathbf{z}\|^2 + \|\mathbf{z} - 3\mathbf{x}\|^2.
\]

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