
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 being separated into piles in the following manner. First, they are randomly divided into two groups. Then, any one of the existing groups is again divided into two groups, and so on until each group consists of one coin. During each division of a group into two, the product of the number of coins in the two resulting groups is recorded. What could be the sum of all the recorded numbers?

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