
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 number $n$ is a three-digit positive integer and is the product of the three distinct prime factors $x$, $y$, and $10x+y$, where $x$ and $y$ are each less than 10. $x$ is an even prime and $y$ is an odd prime. What is the smallest possible value of $n$?

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