
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 $f(x)= \frac{ \sqrt{3}}{2}\cos (2x+\varphi)+\sin^{2}x(0\leq\varphi < \pi)$

(1) If $\varphi= \frac{\pi}{6}$, find the range of $f(x)$;

(2) If the maximum value of $f(x)$ is $\frac{3}{2}$, find the value of $\varphi$.

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