
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
Three candles have the same length but different thicknesses. The first candle was lit 1 hour earlier than the other two, which were lit simultaneously. At some moment, the first and third candles had the same length, and 2 hours after that, the first and second candles had the same length. How many hours does it take for the first candle to burn out if the second candle burns out in 12 hours and the third candle burns out in 8 hours?

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