
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) Simplify: $\dfrac{\sin(\pi -\alpha)\cos(\pi +\alpha)\sin(\dfrac{\pi}{2}+\alpha)}{\sin(-\alpha)\sin(\dfrac{3\pi}{2}+\alpha)}$.

(2) Given $\alpha \in (\dfrac{\pi}{2}, \pi)$, and $\sin(\pi -\alpha) + \cos \alpha = \dfrac{7}{13}$, find $\tan \alpha$.

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