
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
For any natural number, let's call the numbers formed from its digits and have the same "digit" arrangement with the initial number as the "partial numbers". For example, the partial numbers of  $149$  are  ${1, 4, 9, 14,19, 49, 149},$  and the partial numbers of  $313$  are  ${3, 1, 31,33, 13, 313}.$  Find all natural numbers whose partial numbers are all prime. Justify your opinion.

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