
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 $f(x)=3\sin (2x+ \frac {π}{3})$ shifted $\frac {π}{6}$ units to the left and then 1 unit upwards, determine the maximum value of $2x_{1}-x_{2}$ for $x_{1},x_{2} \in [-\frac {3π}{2}, \frac {3π}{2}]$ where $g(x_{1})g(x_{2})=16$.

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