
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 \(a\), \(b\), and \(c\) represent the lengths of the sides of a triangle, with \(\alpha\), \(\beta\), and \(\gamma\) being the angles opposite these sides respectively. Given that \(a^2 + b^2 = 2023c^2\), determine the value of 
\[
\frac{\cot \alpha}{\cot \beta + \cot \gamma}.
\]

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