
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
(1) Find the value of $m$ if the solution set of the inequality $- \frac{1}{2}x^{2}+2x > mx$ with respect to $x$ is $(0,2)$.
(2) In $\triangle ABC$, $\sin A= \frac{5}{13}$ and $\cos B= \frac{3}{5}$. Find the value of $\cos C$.

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