
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
A clerk is inquiring about the residents of an apartment from the superintendent: "How many people live in the apartment?" - "Three." "What are their ages?" - "The product of their ages is 1296." - "That doesn't tell me their ages." - "Then I'll tell you that the sum of their ages is the same as the house number." - "I still can't determine their ages," says the clerk after some thought. - "But do you know how old I am?" -"Yes." - "Well, all of them are younger than I am." - "Thank you, now I know their ages." - Question: How old are the residents?

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