
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 $f(x)=\sin ^{2}2x-\sin 2x\cos 2x$.
(1) Simplify the expression of the function $f(x)$ and find the smallest positive period of the function $f(x)$;
(2) If point $A(x_{0},y_{0})$ is the center of symmetry of the graph of $y=f(x)$, and $x_{0}\in[0, \frac{\pi}{2}]$, find the coordinates of point $A$.

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