
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 the island, there are 2001 inhabitants including liars and knights. Knights always tell the truth, and liars always lie. Each inhabitant of the island declared, "Among the remaining inhabitants of the island, more than half are liars". How many liars are there on the island?

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