
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
Two candles have different initial lengths and burn at different rates. The first candle, which is 10 inches long, burns out completely in 3 hours, while the second candle, which is 12 inches long, burns out completely in 5 hours. Determine the time at which the candles should be lighted if one stub is to be exactly one-third the length of the other at 6 P.M.

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