
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 $ABC$, it is known that $c=13$ and $\cos A = \frac{5}{13}$.

(1) If $a=36$, determine the value of $\sin C$.
(2) If the area of triangle $ABC$ is $6$, find the values of $a$ and $b$.

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