
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 2012 dwarves, each of whom is either good or bad. Every day they attend a meeting in groups of 3 or 5. During each meeting, if the majority of the attendees are good, all attendees of that meeting become good; if the majority are bad, all attendees become bad. If after the third day's meetings all 2012 dwarves have become good, what is the minimum number of good dwarves before the first day's meetings?

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