
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
Boys and girls. Nine boys and three girls decided to share their pocket money equally. Each boy gave the same amount to each girl, and each girl gave the same amount (but a different one) to each boy. After this, all children ended up with an equal amount of money. What is the smallest amount that each of them could have had initially?

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