
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 product of the digits of any multi-digit number is always less than this number. If we calculate the product of the digits of a given multi-digit number, then the product of the digits of this product, and so on, we will necessarily reach a single-digit number after some number of steps. This number of steps is called the persistence of the number. For example, the number 723 has a persistence of 2 because $7 \cdot 2 \cdot 3 = 42$ (1st step) and $4 \cdot 2 = 8$ (2nd step).

1. Find the largest odd number with distinct digits that has a persistence of 1.
2. Find the largest even number with distinct nonzero digits that has a persistence of 1.
3. Find the smallest natural number that has a persistence of 3.

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