
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 \( a_{1}, a_{2}, \ldots, a_{2018} \) be 2018 real numbers such that:

\[ \sum_{i=1}^{2018} a_{i} = 0 \]
\[ \sum_{i=1}^{2018} a_{i}^{2} = 2018 \]

Determine the maximum possible minimum value of the product of any two of these 2018 real numbers.

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