
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
If the graph of the function $f(x)=\sin (2x+\phi )+\sqrt{3}\cos (2x+\phi )$ $(0 < \phi < \pi )$ is translated to the left by $\dfrac{\pi }{4}$ units, and the translated graph is symmetric about the point $\left(\dfrac{\pi }{2},0\right)$, determine the minimum value of the function $g(x)=\cos (x+\phi )$ in the interval $\left[-\dfrac{\pi }{2},\dfrac{\pi }{6}\right]$.

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