
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
We call a natural number \( N \) "bombastic" if it does not contain any zeros in its representation and if no smaller natural number has the same product of digits as \( N \).

Karel was initially interested in bombastic prime numbers and claimed there aren’t many of them. List all two-digit bombastic prime numbers.

Then, Karel chose a bombastic number and revealed to us that it contains the digit 3 and that exactly one of its other digits is even. Which even digit could it be?

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