
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) Simplify $f(x)$ by reducing the power;
(2) Find the minimum value of function $f(x)$ on $\left[\frac{\pi}{16}, \frac{3\pi}{16}\right]$ and find the value of $x$ when $f(x)$ reaches the minimum value.

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