
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 $f(x)=\sin (2017x+\frac{\pi }{6})+\cos (2017x-\frac{\pi }{3})$, find the minimum value of $A|x_{1}-x_{2}|$ where $x_{1}$ and $x_{2}$ are real numbers such that $f(x_{1})\leq f(x)\leq f(x_{2})$ for all real $x$.

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