
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
If the graph of the function $f(x)=\sin (\omega x+\varphi)$ (where $\omega > 0$, $|\varphi| < \frac{\pi}{2}$) is transformed by shrinking all the x-coordinates to half of their original values (keeping the y-coordinates unchanged), and then the resulting graph is shifted to the right by $\frac{\pi}{3}$ units to obtain the graph of $y=\sin x$, then $f(3\pi)=$_______.

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