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

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