
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
Real numbers  $x_1, x_2, \dots, x_{2018}$  satisfy  $x_i + x_j \geq (-1)^{i+j}$  for all  $1 \leq i < j \leq 2018$ .
Find the minimum possible value of  $\sum_{i=1}^{2018} ix_i$ . 

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