
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 $f(x)=\frac{\sqrt{3}}{2}\sin 2x+\cos^2x-\frac{3}{2}$  
(1) Find the smallest positive period of the function $f(x)$ and the interval of monotonic increase.  

(2) When $x\in \left[ 0,\frac{\pi }{2} \right]$, the equation $f(x)-m=0$ has real solutions, find the range of the real number $m$.

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