
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
There is more than one integer greater than $1$ which, when divided by any integer $k$ such that \( 2 \leq k \leq 12 \), has a remainder of $1$. What is the difference between the two smallest such integers?
A) 25080
B) 27720
C) 30240
D) 32400
E) none of these

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