
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
A man left instructions to his executors to distribute once a year exactly fifty-five shillings among the poor of his parish, giving eighteen pence each to a number of women and half a crown each to men. They were only to continue the gift as long as they could make it in different ways, always giving different numbers of men and women each time. During how many years could the charity be administered?

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