
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
We seek the true statement. There are one hundred statements written in a notebook:

1) There is exactly one false statement in this notebook.
2) There are exactly two false statements in this notebook.
...
100) There are exactly one hundred false statements in this notebook.

Which one of these statements is true, given that only one is true?

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