
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 a certain country, there are 2016 deputies, who are divided into 3 factions: "blue," "red," and "green." Each deputy either always tells the truth or always lies. Each deputy was asked three questions:
1) Are you a member of the "blue" faction?
2) Are you a member of the "red" faction?
3) Are you a member of the "green" faction?

1208 deputies responded affirmatively to the first question, 908 deputies responded affirmatively to the second question, and 608 deputies responded affirmatively to the third question. In which faction are there more deputies who lie than those who tell the truth, and by how many?

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