
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 $f\left( x \right)=2\cos \left( 3x+\varphi \right)+3\left( \left| \varphi \right|\leqslant \dfrac{\pi }{2} \right)$, if $\forall x\in \left( -\dfrac{\pi }{6},\dfrac{\pi }{12} \right)$, the graph of $f\left( x \right)$ is always above the line $y=3$, determine the range of $\varphi$.

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