
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 $a$, $b$, $c$ be the sides of a triangle, with angles $\alpha$, $\beta$, $\gamma$ opposite them respectively. Given that $a^2 + b^2 + 32c^2 = 2021c^2$, calculate:
\[
\frac{\cot \gamma}{\cot \alpha + \cot \beta}.
\]

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