
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 of knights and liars, knights always tell the truth, and liars always lie. Knights and liars attend school together in the same class. One day, the teacher asked four children: Anu, Banu, Vanu, and Danu, who among them did their homework. They replied:

- Anu: Banu, Vanu, and Danu did the homework.
- Banu: Anu, Vanu, and Danu did not do the homework.
- Vanu: Don’t believe them, sir! Anu and Banu are liars!
- Danu: No, sir, Anu, Banu, and Vanu are knights!

How many knights are among these children?

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