
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
Initially, the fairy tale island was divided into three counties: in the first county lived only elves, in the second - only dwarves, and in the third - only centaurs.

- During the first year, each county where there were no elves was divided into three counties.
- During the second year, each county where there were no dwarves was divided into four counties.
- During the third year, each county where there were no centaurs was divided into six counties.

How many counties were there on the fairy tale island after all these events?

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