
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 $\triangle ABC$, it is known that $\sin A = \frac{5}{13}$ and $\cos B = \frac{3}{5}$. Determine the value of $\cos C$.
In $\triangle ABC$, if $\tan A$ and $\tan B$ are the roots of the quadratic equation $x^2 + p(x + 1) + 1 = 0$, then find the measure of $\angle C$.

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