
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 $f(x)=2\sin (2x-\frac{\pi }{6})$.

(Ⅰ) Find the intervals of monotonic increase and the equation of the axis of symmetry for the function $f(x)$;

(Ⅱ) When $x\in[0,\frac{\pi }{2}]$, find the maximum and minimum values of the function $f(x)$.

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