
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 $\sin \alpha + \cos \alpha = -\frac{1}{5}$,

(1) Find the value of $\sin (\frac{\pi}{2} + \alpha) \cdot \cos (\frac{\pi}{2} - \alpha)$;

(2) If $\frac{\pi}{2} < \alpha < \pi$, find the value of $\frac{1}{\sin (\pi - \alpha)} + \frac{1}{\cos (\pi - \alpha)}$.

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