
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
Each of the 10 people is either a knight, who always tells the truth, or a liar, who always lies. Each of them picked an integer. Then the first person said, "My number is greater than 1," the second said, "My number is greater than 2," and so on, with the tenth person saying, "My number is greater than 10." After that, all ten, speaking in some order, said one of the following statements: "My number is less than 1," "My number is less than 2," ..., "My number is less than 10" (each person said exactly one of these ten phrases). What is the maximum number of knights that could be among these 10 people?

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