
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 $\overrightarrow{m}=(2\sin \frac {x}{4},\cos \frac {x}{2})$ and $\overrightarrow{n}=(\cos \frac {x}{4}, \sqrt {3})$, and the function $f(x)= \overrightarrow{m}\cdot \overrightarrow{n}$:

(1) Find the smallest positive period of $f(x)$;

(2) If $0\leqslant x\leqslant π$, find the maximum and minimum values of $f(x)$.

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