
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 $\mathbf{a},$ $\mathbf{b},$ $\mathbf{c}$ be vectors such that $\|\mathbf{a}\| = 2,$ $\|\mathbf{b}\| = 3,$ and $\|\mathbf{c}\| = 4.$ Assume $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are pairwise orthogonal. Find the maximum value of
\[
\|\mathbf{a} - 3 \mathbf{b}\|^2 + \|\mathbf{b} - 3 \mathbf{c}\|^2 + \|\mathbf{c} - 3 \mathbf{a}\|^2.
\]

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