
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: \(\cos \left(x-\frac{3 \pi}{2}\right)=-\frac{4}{5}, 0 < x < \frac{\pi}{2}\). Find \(A=\sin \frac{x}{2} \cdot \cos \frac{5 x}{2}\).

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