
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 are split again into two groups, and so on until each group consists of one coin. Each time a group is split into two, the product of the number of coins in the two resulting groups is recorded. What can be the sum of all recorded numbers?

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