
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 $f\left(x\right)=\cos (2x+\frac{π}{3})$, if there exist real numbers $x_{1}$ and $x_{2}$ such that for any real number $x$, $f(x_{1})\leqslant f\left(x\right)\leqslant f(x_{2})$, calculate the minimum value of $|x_{2}-x_{1}|$.

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