
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 $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{c}$ be vectors in a plane such that $\|\mathbf{a}\| = 3$, $\|\mathbf{b}\| = 2$, and $\|\mathbf{c}\| = 4$. Determine 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