
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 12 knights sitting around a round table has chosen a number, and all the numbers are different. Each knight claims that the number they have chosen is greater than the numbers chosen by their neighbors on the right and left. What is the maximum number of these claims that can be true?

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