
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
Let  $a_1,a_2,\dots,a_{2017}$  be reals satisfied  $a_1=a_{2017}$ ,  $|a_i+a_{i+2}-2a_{i+1}|\le 1$  for all  $i=1,2,\dots,2015$ . Find the maximum value of  $\max_{1\le i<j\le 2017}|a_i-a_j|$ .

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