
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 least positive integer greater than $500$ for which
\[\gcd(42, n+80) = 14 \quad \text{and} \quad \gcd(n+42, 80)=40.\]
What is the sum of the digits of $n$?
**A)** 15
**B)** 16
**C)** 17
**D)** 18
**E)** 19

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