
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
There are knights, liars, and followers living on an island; each knows who is who among them. All 2018 islanders were arranged in a row and asked to answer "Yes" or "No" to the question: "Are there more knights on the island than liars?". They answered in turn such that everyone else could hear. Knights told the truth, liars lied. Each follower gave the same answer as the majority of those who answered before them, and if "Yes" and "No" answers were equal, they gave either answer. It turned out that the number of "Yes" answers was exactly 1009. What is the maximum number of followers that could have been among the islanders?

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