
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 has thought of an integer. Then the first person said: "My number is greater than 1," the second said: "My number is greater than 2," ..., the tenth said: "My number is greater than 10." After that, all ten, speaking in a certain order, said: "My number is less than 1," "My number is less than 2," ..., "My number is less than 10" (each 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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