
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 $f(x)=\sin x$, first stretch the horizontal and vertical coordinates of $f(x)$ by a factor of 2, then shift it right by $\frac{\pi}{3}$ units to obtain $y=g(x)$.
(I) Find the analytical expression of function $g(x)$;
(II) Find the interval where function $g(x)$ is increasing.

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