
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 $x_{1}$, $x_{2}$ such that for any real number $x$, $f(x_{1})\leqslant f(x)\leqslant f(x_{2})$ holds, then find the minimum value of $A|x_{1}-x_{2}|$.

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