
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 the function $f(x)=\sin^2x+2\sqrt{3}\sin x\cos x+\sin\left(x+\frac{\pi}{4}\right)\sin\left(x-\frac{\pi}{4}\right)$, if $x=x_0(0\leqslant x_0\leqslant \frac{\pi}{2})$ is a zero of the function $f(x)$, then $\cos 2x_0=$ ______.

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