
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 equally long candles were lit simultaneously. One burns completely in 3 hours, while the other burns completely in 5 hours. In a photo, the ratio of the lengths of the two candles is $1:2$, in another photo it is $1:3$, and in a third photo it is $1:4$. When were each of the photos taken? - In another similar pair of candles, one candle - we don't know which one - is lit half an hour before the other. When can we expect the length ratios to again be $1:2, 1:3$, and $1:4$? - Let's also look for a graphical solution.


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