
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 $f(x)=\sin (2x+ \frac {\pi}{3})+\cos (2x+ \frac {\pi}{6})+2\sin x\cos x$.
- (I) Find the equation of the axis of symmetry for the graph of function $f(x)$.
- (II) Translate the graph of the function $y=f(x)$ to the right by $\frac {\pi}{12}$ units, then stretch the x-coordinates of the obtained graph by a factor of $4$ while keeping the y-coordinates unchanged, to get the graph of the function $y=g(x)$. Find the range of $y=g(x)$ on $[\frac {\pi}{3},2\pi]$.

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