
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 a set $A=\{a_1, a_2, \ldots, a_n\}$ where all elements are positive integers, and $a_1 < a_2 < \ldots < a_n$, set $A$ has property $P$: for any $x, y \in A$ and $x \neq y$, it holds that $|x-y| \geq \frac{xy}{25}$. Consider the following statements:  
① The set $\{1, 2, 3, 4\}$ does not have property $P$;  
② $\frac{1}{a_1} - \frac{1}{a_n} \geq \frac{n-1}{25}$;  
③ The inequality $i(n-i) < 25$ holds for $i=1, 2, \ldots, n-1$;  
④ The set $A$ can have at most 10 elements.  
The correct statement(s) is/are __________ (Fill in all correct statement numbers).

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