
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 $0 < \alpha < \frac{\pi}{2}$, calculate the following:
1. The value of $\sin \alpha + \cos \alpha$ given $ \cos(2\pi - \alpha) - \sin(\pi - \alpha) = -\frac{\sqrt{5}}{5}$.
2. The value of $\frac{\cos^2\left( \frac{3\pi}{2} + \alpha \right)+ 2 \cos \alpha \cos\left( \frac{\pi}{2} - \alpha \right)}{1 + \sin^2\left( \frac{\pi}{2} - \alpha \right)}$.

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