
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 the parliament of the island nation Promenade-and-Tornado, only native inhabitants, who are divided into knights and liars, can be elected. Knights always tell the truth, and liars always lie. In the latest term, 2020 deputies were elected. At the first plenary session of the parliament, 1011 deputies declared: "If you do not count me, there are more liars than half among the remaining deputies." How many liars are there in the parliament of this nation?

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