
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 three factors: $x$, $y$, and $10x+y$, where $x$ is a prime digit, $x + y$ is not a multiple of 3, and $10x+y$ forms a prime number. What is the largest possible value of $n$ given these conditions?

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