
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
Positive real numbers  $a_1, a_2, \ldots, a_{2024}$  are arranged in a circle. It turned out that for any  $i = 1, 2, \ldots, 2024$ , the following condition holds:  $a_ia_{i+1} < a_{i+2}$ . (Here we assume that  $a_{2025} = a_1$  and  $a_{2026} = a_2$ ). What largest number of positive integers could there be among these numbers  $a_1, a_2, \ldots, a_{2024}$ ?

*Proposed by Mykhailo Shtandenko*

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