
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 vectors $\overrightarrow{a}=(1,\cos \alpha )$ and $\overrightarrow{b}=(-2,\sin \alpha )$, and $\overrightarrow{a}\parallel\overrightarrow{b}$.

$(1)$ Find the value of $\tan (\pi +\alpha )$;

$(2)$ Find the value of $3\sin^2\alpha -\sin (2\pi -\alpha )\cos \alpha$.

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