
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
Determine the smallest integer greater than $1$ which, when divided by any prime $k$ less than $13$ or by $15$, leaves a remainder of $2$. What is the difference between the two smallest such integers?
A) 2100
B) 2310
C) 4620
D) 27720
E) None of these

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