
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, B, and C are mathematicians. D asks the others—one of whom is quite absent-minded—about their ages. They decide to provide information that determines their age using a numeral system other than the decimal system.

A says: "Take four numbers in sequence with a difference of 2 between each. Write the next number after the smallest one. The resulting number, interpreted as a two-digit number in a certain numeral system, gives my age; and it is the same as the product of the two largest numbers."

B states that his age can be obtained by writing two consecutive numbers next to each other (starting with the smaller one), and this number is a two-digit number in a numeral system whose value is the product of the two consecutive numbers following the selected pair.

Finally, C, the youngest, declares that regarding his age, he can say the same as what A stated about his own age.

Now D was able to determine the ages of A, B, and C, as well as who is the absent-minded one.

Let's determine their ages and identify who the absent-minded mathematician is!

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