
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
I had 100 francs in denominations of 1 franc, 5 francs, and 50 centimes. Now I have none, as I gave all the 1-franc coins to Victor, all the 5-franc coins to Marguerite, and all the 50-centime coins to Gustav. What is the smallest share that one of my children received if one of the boys received nine times fewer coins than the other?

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