
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 $f(x)=2\sin x$, the graph of the function $y=f(x)$ is translated to the right by $\frac{\pi}{6}$ units, and then the horizontal coordinate is compressed to $\frac{1}{2}$ of its original length (the vertical coordinate remains unchanged) to obtain the graph of the function $y=g(x)$. Find the analytical expression of the function $y=g(x)$ and write out its monotonically increasing interval.

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