
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 $\tan \alpha = \frac{1}{3}$, calculate the value of $\frac{1}{2\sin \alpha \cos \alpha + \cos^2 \alpha}$;  
(2) Simplify: $\frac{\tan(\pi - \alpha)\cos(2\pi - \alpha)\sin(-\alpha + \frac{3\pi}{2})}{\cos(-\alpha - \pi)\sin(-\pi - \alpha)}$.

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