
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
In an arithmetic sequence \(a_1, a_2, \ldots, a_{1990}\) with a non-zero common difference, where \(a_i a_j > 0\) for all \(i, j = 1, 2, \ldots, 1990\), let \(b_1 = a_1 \cdot a_{1990}\), \(b_2 = a_2 \cdot a_{1989}\), \(\ldots\), \(b_k = a_k \cdot a_{1990 - k + 1}\) for \(k = 1, 2, \ldots, 1990\). Then, the largest term among \(\{b_k\}\) is \(\qquad\) .

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