
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 $\overrightarrow{a}=( \frac{1}{2}, \frac{1}{2}\sin x+ \frac{ \sqrt{3}}{2}\cos x)$ and $\overrightarrow{b}=(1,f(x))$, and $\overrightarrow{a}//\overrightarrow{b}$.
(1) Find the minimum positive period and maximum value of the function $f(x)$;
(2) If the three internal angles of $\triangle ABC$ are $A$, $B$, and $C$, respectively, and $f(2A- \frac{π}{6})=1$, $BC= \sqrt{7}$, $\sin B= \frac{ \sqrt{21}}{7}$, find the length of $AC$.

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