
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
Let the line \( y = a \) intersect the curve \( y = \sin x \) (for \( 0 \leqslant x \leqslant \pi \)) at points \( A \) and \( B \). If \( |AB| = \frac{\pi}{5} \), find the value of \( a \) (accurate to 0.0001).

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