
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
16 travelers, each of whom is either a liar or a knight (liars always lie, knights always tell the truth), settled into 3 hotel rooms. When everyone gathered in their rooms, Vasily, residing in the first room, said: "There are more liars in this room than knights. No, wait - there are more knights in this room than liars." After that, Vasily entered the second room and repeated the same two statements there. Then he entered the third room and also said the same two statements. What could be the number of knights among these 16 travelers?

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