
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 $f(x)=A\sin (2x+\varphi)-\dfrac{1}{2}$ $(A > 0,0 < \varphi < \dfrac{\pi}{2})$ whose graph intercepts the $y$-axis at $1$, and is symmetric about the line $x=\dfrac{\pi}{12}$. If for any $x\in[0,\dfrac{\pi}{2}]$, it holds that $m^{2}-3m\leqslant f(x)$, calculate the range of the real number $m$.

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