
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 real numbers \( x_{1}, x_{2}, \cdots, x_{2018} \) such that for any \( 1 \leqslant i < j \leqslant 2018 \), we have \( x_{i} + x_{j} \geqslant (-1)^{i+j} \). Find the minimum value of \( \sum_{i=1}^{2018} i x_{i} \).

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