
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 $f(x) = 2\sqrt{3}\sin x\cos x + \cos 2x + 3$ ($x \in \mathbb{R}$).
1. Determine the smallest positive period of the function $f(x)$.
2. Find the maximum value of the function $f(x)$ in the interval $\left[0, \frac{\pi}{4}\right]$ and the corresponding value of $x$ when the maximum value is attained.

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