
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 $f(x)=2 \sqrt {3}\sin x\cos x+1-2\sin ^{2}x$, where $x\in R$.
(1) Find the minimum positive period and the monotonically increasing interval of the function $f(x)$;
(2) Keep the vertical coordinates of each point on the graph of the function $y=f(x)$ unchanged, shorten the horizontal coordinates to half of the original, and then move the obtained graph to the left by $\frac {\pi}{6}$ units to obtain the graph of the function $y=g(x)$. Find the minimum value of the function $y=g(x)$ on the interval $[0, \frac {\pi}{8}]$.

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