
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 vectors $\overrightarrow{a}=(2\cos x,1)$ and $\overrightarrow{b}=(\cos x,\sqrt{3}\sin 2x)$, where $x\in R$. Define function $f(x)=\overrightarrow{a}\cdot\overrightarrow{b}$. Find:

1. The smallest positive period of $f(x)$;
2. The maximum value of $f(x)$ and the value of $x$ when the maximum is attained.

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