
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 $\sin \alpha \tan \alpha = \frac{3}{2}$, and $0 < \alpha < \pi$.
(1) Find the value of $\alpha$;
(2) Find the range of the function $f(x)=4\cos x\cos (x-\alpha)$ on $\[0, \frac{\pi}{4}\]$.

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