
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 $f(x)=\sin \left(x-\frac {\pi}{6}\right)$, transform the graph by making the x-coordinates of all points half of their original values and then shifting the newly obtained graph to the right by $\frac {\pi}{3}$ units to get the graph of $y=g(x)$. When $x\in\left( \frac {\pi}{4}, \frac {3\pi}{4}\right)$, determine the range of the function $g(x)$.

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