
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 $f(x)=2\sin (\omega x- \frac {\pi}{8})$ ($\omega > 0$), shift the graph to the left by $\frac {\pi}{8\omega }$ units to obtain the graph of the function $y=g(x)$, and if $y=g(x)$ is increasing on the interval $\left[0, \frac {\pi}{4}\right]$, determine the maximum value of $\omega$.

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