
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 knights who always tell the truth and liars who always lie.

One day, 10 inhabitants of the island gathered, each wearing a T-shirt numbered from 1 to 10 (each inhabitant has a different number). Every one of them made one of the following statements:

- "There is no knight among those gathered whose T-shirt number is greater than mine."
- "There is no liar among those gathered whose T-shirt number is less than mine."

It is known that each of these statements was made exactly 5 times. How many knights could there be among these 10 inhabitants? List all possible options.

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