
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  $N=\overline{abcd}$  be a positive integer with four digits. We name *plátano power* to the smallest positive integer  $p(N)=\overline{\alpha_1\alpha_2\ldots\alpha_k}$  that can be inserted between  the numbers  $\overline{ab}$  and  $\overline{cd}$  in such a way the new number  $\overline{ab\alpha_1\alpha_2\ldots\alpha_kcd}$  is divisible by  $N$ . Determine the value of  $p(2025)$ .

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