
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 $2000$ for which:
\[\gcd(75, n+135) = 15\quad \text{and} \quad \gcd(n+75, 135) = 45.\]
What is the sum of the digits of $n$?
A) 7
B) 9
C) 10
D) 12

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