
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
Dr. Math's five-digit house number $ABCDE$ contains no zeroes. It can be split into a two-digit prime $AB$ and a three-digit prime $CDE$, where the digits $A$, $B$, $C$, $D$, and $E$ are not necessarily distinct. If each prime, $AB$ and $CDE$, is less than 100 and 500 respectively, how many such house numbers are possible?

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