
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
The sequence {a<sub>n</sub>} is an arithmetic sequence with a non-zero common difference, and a<sub>i</sub> ∈ [0, 4], 1 ≤ i ≤ 2019. The function f(x) = 3sin( $$\frac {π}{4}$$x - $$\frac {π}{2}$$). If f(a<sub>1</sub>) + f(a<sub>2</sub>) + f(a<sub>3</sub>) + ... + f(a<sub>2019</sub>) = 0, then a<sub>1</sub> + a<sub>2</sub> + a<sub>3</sub> + ... + a<sub>2019</sub> = _____.

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