
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 $f(x)=2\sin^4x+2\cos^4x+\cos^22x-3$.  
(1) Find the smallest positive period of the function $f(x)$.  
(2) Find the minimum value of the function $f(x)$ in the closed interval $\left[\frac{\pi}{16}, \frac{3\pi}{16}\right]$ and the set of values of $x$ when $f(x)$ takes its minimum value.

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