
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 $f(x) = (\sin x + \cos x)^2 + \cos 2x$,  
(1) find the smallest positive period of $f(x)$;  
(2) find the maximum and minimum values of $f(x)$ on the interval $\left[\frac{\pi}{4}, \frac{3\pi}{4}\right]$.

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