
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
If $\frac{\sin (\pi -\alpha )\cos (2\pi -\alpha )}{\tan (\pi -\alpha )\sin (\frac{\pi }{2}+\alpha )\cos (\frac{\pi }{2}-\alpha )}=\frac{1}{2}$, find:

(1) $\frac{\cos \alpha -2\sin \alpha }{3\cos \alpha +\sin \alpha }$;

(2) The value of $1-2\sin \alpha \cos \alpha +{{\cos }^{2}}\alpha$.

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