
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
In the Cartesian coordinate system, the initial side of angle \(a\) lies on the non-negative half-axis of the \(x\)-axis, and there is a point on the terminal side that is \((1, \sqrt{3})\). If \(a \in [0,2\pi)\), then \(\int_{-a}^{a}{\cos xdx}=\)_______.

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