
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 $\frac{3\sin \alpha - \cos \alpha}{2\sin \alpha + 3\cos \alpha} = \frac{5}{7}$:

1. Find the value of $\tan (\frac{\pi}{2} - \alpha)$;
2. Find the value of $3\cos \alpha \cdot \sin (\alpha + \pi) + 2\cos^2 (\alpha + \frac{\pi}{2})$.

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