
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
In a certain book, there were 100 statements written as follows:
1) "In this book, there is exactly one false statement."
2) "In this book, there are exactly two false statements."
...
3) "In this book, there are exactly one hundred false statements."

Which of these statements is true?

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