
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
Shifting the graph of the function $f(x) = 2\sin 2x$ to the right by $\frac{\pi}{3}$ units and then upwards by $1$ unit results in the graph of the function $g(x)$. Determine the range of $g(x)$ in the interval $\left[ -\frac{\pi}{3},\frac{\pi}{2} \right]$.

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