
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
On an island, there are vegetarians who always tell the truth, and cannibals who always lie. 50 islanders, both women and men, gathered around a campfire. Each of them said either "All men at this campfire are cannibals" or "All women at this campfire are vegetarians", and both statements were made. What is the maximum number of vegetarian women that could have been at the campfire?

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