
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 a certain island, there are 10 people. Some of them always tell the truth, while others always lie. Each person has thought of a real number (not necessarily an integer). The first person says, "My number is greater than 1." The second person says, "My number is greater than 2," and so on up to the tenth person who says, "My number is greater than 10." After that, these ten people stand in a line in some order, and each one then says, "My number is less than 1," "My number is less than 2," and so on up to "My number is less than 10" (each person speaks exactly once). The question is: What is the maximum number of truth-tellers among these people?

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