
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 exactly three distinct prime numbers $d$, $e$, and $d^2 + e^2$, where $d$ and $e$ are distinct single-digit primes such that $d < e$. Find the sum of the digits of $n$.

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