
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. Given $\tan \alpha=2$, find the value of $\sin ^{2}( \frac {\pi}{2}-\alpha)+3\sin (\alpha+\pi)\sin (\alpha+ \frac {\pi}{2})$;
2. Given that $\alpha$ is an angle in the second quadrant and its terminal side passes through point $P(a,1)$, and $\cos \alpha= \frac{ \sqrt {2}}{4}a$, find the value of the real number $a$.

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