
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 $f(x)=\sin ^{2}x+2 \sqrt {3}\sin x\cos x+\sin (x+ \frac {π}{4})\sin (x- \frac {π}{4}).$
(1) Find the interval(s) where $f(x)$ is increasing;
(2) If $x_{0}$ is a zero of $f(x)$ ($0\leqslant x_{0}\leqslant \frac {π}{2}$), find the value of $\cos 2x_{0}$.

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