
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 company, there are elves, fairies, and dwarves. Each elf is friends with all fairies except for three of them, and each fairy is friends with twice as many elves. Each elf is friends with exactly three dwarves, and each fairy is friends with all the dwarves. Each dwarf is friends with exactly half of the total number of elves and fairies. How many dwarves are there in the company?

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