
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 $f(x)=4\sin (\frac{\pi }{3}x+\frac{\pi }{4})$, if for all $x\in R$ we have $f({{x}\_{1}})\leqslant f(x)\leqslant f({{x}\_{2}})$, determine the minimum value of $|{{x}\_{1}}-{{x}\_{2}}|$.

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