
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, 80 islanders gathered, each wearing a T-shirt numbered from 1 to 80 (with different numbers for each resident). Each of them said one of two phrases:

- "Among the gathered, at least 5 liars have a T-shirt number greater than mine."
- "Among the gathered, at least 5 liars have a T-shirt number less than mine."

What is the minimum number of knights that could be among these 80 residents?

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