
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 a newly discovered planet, there are animals named according to their number of legs: one-leggers, two-leggers, three-leggers, etc. (animals with no legs were not found). Animals with an odd number of legs have two heads, and animals with an even number of legs have one head. In a certain hollow, astronauts encountered a group of these animals and counted 18 heads and 24 legs.

How many animals could be in the hollow? Determine all possibilities.


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