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

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