
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, there are knights, who always tell the truth, and liars, who always lie. There are 15 islanders in a room. Each of the islanders in the room made two statements: "Among my acquaintances in this room, there are exactly six liars" and "Among my acquaintances in this room, there are no more than seven knights". How many knights can be in this room?

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