
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. In a school on this island, both knights and liars study in the same class. One day the teacher asked four children: Anu, Banu, Vanu, and Danu, who among them did the homework. They responded:

- Anu: Banu, Vanu, and Danu did the homework.
- Banu: Anu, Vanu, and Danu did not do the homework.
- Vanu: Do not believe them, teacher! Anu and Banu are liars!
- Danu: No, teacher, 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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