
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 that $\alpha$ is an angle in the second quadrant and $\sin \alpha = \frac{3}{5}$, find the value of $\frac{1 + \sin \alpha + \cos \alpha + 2 \sin \alpha \cos \alpha}{1 + \sin \alpha + \cos \alpha}$.

(2) Given that $\alpha$ is an angle in the second quadrant, simplify the expression: $\cos \alpha \sqrt{\frac{1 - \sin \alpha}{1 + \sin \alpha}} + \sin \alpha \sqrt{\frac{1 - \cos \alpha}{1 + \cos \alpha}}$.

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