
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 $f(x)=\sin 2x$, the graph of function $f(x)$ is translated right by $\dfrac{\pi}{6}$ units and then translated up by $\dfrac{\sqrt{3}}{2}$ units to obtain the graph of function $g(x)$. Determine the range of function $g(x)$ when $x\in[0, \dfrac{\pi}{2}]$.

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