
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 $c$ be the sides of a triangle with angles $\alpha$, $\beta$, and $\gamma$ opposite them respectively. Suppose $a^2 + b^2 = 9c^2$. Find the value of
\[\frac{\tan \gamma}{\tan \alpha + \tan \beta}.\]

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