
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
The monkey tells the fox:

- Do you see the 3 people running over there? I know that the product of their ages is 2450 and that the sum of their ages is double your age. Can you tell me their ages?
- No, responds the fox.
- If I tell you that the youngest of the three is the only blonde, can you now determine their ages?

And the fox gives the ages of the 3 people.

Why can't the fox answer initially? And why can she answer afterward?

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