
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 $\mathbf{p}$, $\mathbf{q}$, $\mathbf{r}$ be vectors such that $\|\mathbf{p}\| = 2$, $\|\mathbf{q}\| = 1$, and $\|\mathbf{r}\| = 3$. Find the maximum value of
\[
\|\mathbf{p} - 3\mathbf{q}\|^2 + \|\mathbf{q} - 3\mathbf{r}\|^2 + \|\mathbf{r} - 3\mathbf{p}\|^2.
\]

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