
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 $x$, $y$, $z$ be the three sides of a triangle, and let $\xi$, $\eta$, $\zeta$ be the angles opposite them, respectively. Given that $x^2+y^2=2023z^2$, find the value of
\[\frac{\cot \zeta}{\cot \xi+\cot \eta}.\]

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