
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

Twenty-five coins are divided into piles in the following way. First, they are randomly split into two groups. Then any of the existing groups is split into two groups again, and this process continues until each group consists of just one coin. Each time a group is split into two groups, the product of the number of coins in the two resulting groups is recorded. What could the sum of all the recorded numbers be?

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