
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 an arithmetic sequence $\{a_{n}\}$ (with a non-zero common difference) and the sum of the first $n$ terms of an arithmetic sequence $\{b_{n}\}$ are $S_{n}$ and $T_{n}$, respectively, determine the maximum number of equations of the form $x^{2}-a_{i}x+b_{i}=0$ among the 2023 equations for which it has no real solutions.

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