
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 that $\sin \alpha= \frac{ \sqrt {5}}{5}$ and $\alpha$ is an angle in the second quadrant.
(1) Find the value of $\tan \alpha$;
(2) Find the value of $\sin \alpha \cdot \cos \alpha - \cos^2 \alpha$;
(3) Find the value of $\frac{\sin(\frac{\pi}{2}-\alpha)\cos(-\alpha-\pi)}{\cos(-\pi+\alpha)\cos(\frac{\pi}{2}+\alpha)}$.

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