
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 2018 real numbers \(a_1, a_2, \ldots, a_{2018}\) satisfying
$$
\sum_{i=1}^{2018} a_i = 0, \quad \sum_{i=1}^{2018} a_i^2 = 2018,
$$
find the maximum possible value of the minimum product of any two of these numbers.

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