
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. The island's football team has 11 players. Player number 1 said: "In our team, the number of knights and the number of liars differs by one." Player number 2 said: "In our team, the number of knights and the number of liars differs by two," and so on. Player number 11 said: "In our team, the number of knights and the number of liars differs by eleven." How many knights are on the team, and if there are any, what are their numbers?

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