
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
Let $n$ be the largest integer that is the product of two distinct digits $d$ and $e$, and the smallest multiple of any prime $k$ ($k > d, k > e$), where $k = 10d + e$. Additionally, ensure the sum $d+e$ is a prime number. What is the sum of the digits of $n$?
A) 6
B) 9
C) 12
D) 15
E) 18

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