
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 $f(x)=|x+1|+|x+2|+\cdots+|x+2017|+|x-1|+|x-2|+\cdots+|x-2017| (x\in \mathbb{R})$, and $f(3a+1)=f(2a+2)$, then the set of all real numbers $a$ that satisfy the condition is __________.

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