
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

There are 30 people standing in a row, each of them is either a knight who always tells the truth or a liar who always lies. They are numbered from left to right. Each person with an odd number says: "All people with numbers greater than mine are liars", and each person with an even number says: "All people with numbers less than mine are liars".

How many liars could there be? If there are multiple correct answers, list them in ascending order separated by semicolons.

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