
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 point  $P_1, P_2,\cdots ,P_{2018} $  is placed inside or on the boundary of a given regular pentagon. Find all placement methods are made so that   $$ S=\sum_{1\leq i<j\leq 2018}|P_iP_j| ^2 $$  takes the maximum value.

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