
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
In a group of 50 children, each child has all their siblings in the group. Each child with no older siblings announces the number of siblings they have, while each child with an older sibling says they have 0 siblings. The average of the numbers everyone announces is \(\frac{12}{25}\). Compute the number of different sets of siblings represented in the group.

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