
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 $\triangle ABC$, the sides opposite to angles A, B, and C are $a$, $b$, and $c$ respectively. Given that $\sin A + \sin B = \frac{5}{4} \sin C$, and the perimeter of $\triangle ABC$ is 9, and the area of $\triangle ABC$ is $3 \sin C$, find $c$ and $\cos C$.

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