
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 $f(x)=2a\sin \omega x\cos \omega x+2 \sqrt {3}\cos ^{2}\omega x- \sqrt {3}$ ($a > 0$, $\omega > 0$) has a maximum value of $2$, and its smallest positive period is $\pi$.

(I) Find the analytical expression of the function $f(x)$ and the equation of its axis of symmetry;

(II) If $f(\alpha)= \frac {4}{3}$, find the value of $\sin (4\alpha+ \frac {\pi}{6})$.

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