
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 $\cos \alpha \sin \alpha = \frac{1}{8}$ and $\frac{\pi}{4} < \alpha < \frac{\pi}{2}$,
(1) find the value of $\tan \alpha$;
(2) find the value of $\frac{2\sin \alpha + 3\cos \alpha}{\sin \alpha + \cos \alpha}$;
(3) find the value of $\frac{1}{\cos^2 \alpha + \sin 2\alpha}$.

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