
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 $a = \int_{-1}^1 \sqrt{1-x^2} \, dx$, find the constant term in the expansion of $\left[ (a + 2 - \frac{\pi}{2})x - \frac{1}{x}\right]^{6}$.

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