
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 x₁ and x₂ such that for any real number x, f(x₁) ≤ f(x) ≤ f(x₂) always holds, calculate the minimum value of A|x₁ - x₂|.

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