
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
If $\theta$ is an acute angle and \( \sin 2\theta = a \), find the value of \( \sin\theta \cdot \cos\theta \).
**A)** \( \frac{\sqrt{a}}{2} \)
**B)** \( \frac{a}{2} \)
**C)** \( \frac{2}{a} \)
**D)** \( \frac{a}{4} \)

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