
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 as the product of exactly 3 distinct primes $d$, $e$, and $9d+e$, where $d$ and $e$ are single-digit primes. Among these primes, $d$ can only be one of $\{3, 5, 7\}$. Find the sum of the digits of $n$.
A) 9
B) 10
C) 11
D) 12
E) 13

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