
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 the Isle of Logic, there live 40 knights (who always tell the truth), 25 liars (who always lie), and a few sophists. A sophist can only make statements that neither a knight nor a liar could make in his position. For example, when standing next to a liar, a sophist might say, "We are both liars" (because if he were a knight, the statement would be a lie, and if he were a liar, it would be the truth). One day, a sophist made two statements about the inhabitants of the island:

1. "There are exactly ... knights on the island."
2. "There are exactly ... liars on the island."

Restore both statements made by the sophist.

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