
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 paper, we can read the following 100 statements:

1. Exactly one statement on this paper is false.
2. Exactly two statements on this paper are false.
3. Exactly three statements on this paper are false.
...
100. Exactly 100 statements on this paper are false.

Determine which statements on the paper are true.

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