
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 arranged into piles as follows. First, they are randomly divided into two groups. Then, any of the existing groups is further divided into two groups, and this continues until each group consists of only one coin. Every time a group is divided into two, the product of the number of coins in the two resulting groups is recorded. What can the sum of all the recorded numbers be?

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