
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 $f(x)=2\sin (180^{\circ}-x)+\cos (-x)-\sin (450^{\circ}-x)+\cos (90^{\circ}+x)$,

(1) If $f(\alpha)= \frac{2}{3}, \alpha \in (0^{\circ},180^{\circ})$, find $\tan \alpha$;

(2) If $f(\alpha)=2\sin \alpha-\cos \alpha+ \frac{3}{4}$, find the value of $\sin \alpha \cdot \cos \alpha$.

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