
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
Vasya has thought of six natural numbers: \( a, b, c, d, e, f \). For one ruble, it is possible to specify any two of them and find out their product. Petya knows that any two of the thought numbers are coprime (i.e., they have no common divisors greater than 1). For what minimum amount can he find out all the thought numbers?

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