
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 $f(x)=2\cos x\sin (x+ \frac {π}{3})- \sqrt {3}\sin ^{2}x+\sin x\cos x$,
(1) Find the smallest positive period of the function $f(x)$;
(2) Find the minimum value of $f(x)$ and the corresponding value of $x$;
(3) If $x∈[\frac {π}{12}, \frac {7π}{12}]$ when $f(x)$ has an inverse function $f^{-1}(x)$, find the value of $f^{--1}(1)$.

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