
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
The graph of the function $y=2\cos\left(x-\frac{\pi}{3}\right)$ is shifted to the right by $m\left(0 \lt m \lt \pi \right)$ units to obtain the graph of $f(x)$. If $f(x)$ is monotonically increasing on $\left(\frac{\pi}{6},\frac{5\pi}{6}\right)$, determine the range of values for $m$.

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