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

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