
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
Given $f(\alpha)= \frac{1+\sin \left(-\alpha\right)+\sin^{2}\left(2\pi-\alpha\right)-\sin^{2}\left( \frac{\pi}{2}+\alpha\right)}{2\sin \left(\pi-\alpha\right)\sin \left( \frac{\pi}{2}-\alpha\right)+\cos \left(\pi+\alpha\right) }$.

(1) Simplify the expression of $f(\alpha)$;

(2) If $f(\alpha)=2$, find the value of $(\_\sin\_\alpha+$\_$\cos\_\alpha)\cos\_\alpha$.

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