
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 $f(x)=2\sin (2x+\frac{\pi }{3} )+1$,

(1) If the graph of the function $y=f(x)$ is symmetric about the line $x=t(t > 0)$, find the minimum value of $t$;

(2) If the equation $mf(x_{0})-2=0$ has two solutions in $x_{0}\in[-\frac{\pi }{12},\frac{\pi }{6} ]$, find the range of values for the real number $m$;

(3) If there exists an interval $[a,b]$ ($a$, $b\in R$ and $a < b$) such that $y=f(x)$ has at least 6 zeros in $[a,b]$, find the minimum value of $b-a$.

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