
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 a function $y=f(x)$, its graph is transformed in the following way: first, it is translated $\frac{\pi}{6}$ units to the left, then the abscissa of all points on the resulting graph is stretched to twice its original length while the ordinate remains unchanged, and finally, the resulting graph is translated 1 unit upward to obtain the graph of the function $y=\sin x$.
(I) Find the analytical expression of the function $y=f(x)$;
(II) If the graph of the function $y=g(x)$ is symmetric to the graph of $y=f(x)$ about the point $M(\frac{\pi}{4}, 2)$, find the minimum and maximum values of the function $y=g(x)$ on the interval $[0, \frac{\pi}{2}]$.

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