
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
Three brothers returned from fishing. Their mother asked each of them how many fish they caught together. Vasya said, "More than ten," Petya said, "More than eighteen," and Kolya said, "More than fifteen." How many fish could have been caught (list all possibilities), knowing that two brothers told the truth and one lied?

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