
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 $f(x)=a\sin x+b\cos x(a,b\in\mathbb{R})$, the equation of the tangent line to the curve $y=f(x)$ at the point $\left( \frac {\pi}{3},f( \frac {\pi}{3})\right)$ is: $y=x- \frac {\pi}{3}$.  
(I) Find the values of $a$ and $b$;  
(II) Find the minimum value of the function $g(x)= \frac {f(x+ \frac {\pi}{3})}{x}$ on the interval $(0, \frac {\pi}{2}]$.

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