
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 state, 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 the following three questions:
1) Are you in the "blue" faction?
2) Are you in the "red" faction?
3) Are you in the "green" faction?

1208 deputies answered "yes" to the first question, 908 deputies answered "yes" to the second question, and 608 deputies answered "yes" 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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