
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
Shift the graph of the function $f(x)=2\sin (2x- \frac {\pi}{6})$ to the left by $\frac {\pi}{6}$ units, and then shift it upwards by $1$ unit to obtain the graph of $g(x)$. If $g(x_{1})+g(x_{2})=6$, and $x_{1}, x_{2} \in [-2\pi, 2\pi]$, then the maximum value of $x_{1}-x_{2}$ is $\boxed{\text{C: } 3\pi}$.

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