
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
Knights, who always tell the truth, and liars, who always lie, live on an island. One day, 100 residents of this island lined up, and each of them said one of the following phrases:

- "To the left of me there are as many liars as knights."
- "To the left of me there is 1 more liar than knights."
- "To the left of me there are 2 more liars than knights."
- "To the left of me there are 99 more liars than knights."

It is known that each phrase was said by exactly one person. What is the minimum number of liars that can be among these 100 residents?

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