
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
Find the difference between two smallest integers greater than $2$ which, when divided by any integer $k$ such that $2 \le k \le 12$, have a remainder of $2$.
A) 13,860
B) 27,720
C) 38,652
D) 55,440
E) None of these

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