
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 that the maximum value of the function $f(x)=\sin(2019x+ \frac {π}{6})+\cos(2019x- \frac {π}{3})$ is A. If there exist real numbers $x_1$, $x_2$ such that for any real number $x$, $f(x_1) \leq f(x) \leq f(x_2)$ always holds, then the minimum value of $A|x_1-x_2|$ is ___.

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