
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 $p$, $q$, $r$ be the sides of a triangle, and let $\theta$, $\phi$, $\psi$ be the angles opposite these sides respectively. Suppose that $p^2 + q^2 = 2001r^2$. Find the value of
\[\frac{\cot \psi}{\cot \theta + \cot \phi}.\]

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