
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 $f(x) = \sqrt{3}\sin (2017x)+\cos (2017x)$, its maximum value is $A$. If there exist real numbers $x_1$ and $x_2$ such that for any real number $x$, $f(x_1) \leqslant f(x) \leqslant f(x_2)$ holds true, calculate the minimum value of $2A|x_1-x_2|$.

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