
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
Translate the graph of the function $f(x)=2\sin (\omega x+ \frac {\pi}{3})$ ($\omega > 0$) to the right by $\frac {\pi}{3\omega }$ units to obtain the graph of the function $y=g(x)$. If $y=g(x)$ is increasing on the interval $\left[0, \frac {\pi}{4}\right]$, then the maximum value of $\omega$ is \_\_\_\_\_\_.

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