
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 \(\triangle ABC\), let \(BC = a\), \(CA = b\), \(AB = c\). If \(9a^{2} + 9b^{2} - 19c^{2} = 0\), then \(\frac{\cot C}{\cot A + \cot B} =\)

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