
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 $a>0$, the constant term in the expansion of $\left( \frac{a}{\sqrt{x}} - x \right)^6$ is 15. Find the value of $$\int_{-a}^{a} \left( \sqrt{1-x^2} + \sin 2x \right) dx.$$

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