
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
In triangle $PQR$, the side lengths $p$, $q$, and $r$ satisfy $p + 3q + 3r = p^2$ and $p + 3q - 3r = 3$. Find the largest angle of the triangle, assuming $p$ is opposite $\angle P$, $q$ opposite $\angle Q$, and $r$ opposite $\angle R$.

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