
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 $f(x)=2\sin (\omega x+\varphi -\frac{\pi }{6})(\omega > 0,0 < \varphi < \pi )$ is an even function, and the distance between two adjacent axes of symmetry of the graph of $f(x)$ is $\frac{\pi}{2}$.

(Ⅰ) Find the analytical expression of $f(x)$;  

(Ⅱ) Find the range of $f(x)$ in the interval $\left[-\frac{\pi }{8},\frac{3\pi }{8}\right]$.

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