
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 $f(x)= \sqrt {3}\sin \omega x+\cos \omega x (\omega > 0)$, the distance between two adjacent intersections of the graph of $f(x)$ with the $x$-axis is $\dfrac {\pi}{2}$. If the graph of the function $y=f(x)$ is translated to the right by $\dfrac {\pi}{12}$ units to obtain the graph of the function $y=g(x)$, determine the maximum value of the function $y=g(x)$ in the interval $\left[ \dfrac {\pi}{12}, \dfrac {\pi}{3}\right]$.

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