
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
One day in a room there were several inhabitants of an island where only truth-tellers and liars live. Three of them made the following statements:

- There are no more than three of us here. We are all liars.
- There are no more than four of us here. Not all of us are liars.
- There are five of us here. Three of us are liars.

How many people are in the room and how many of them are liars?

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