
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 \( L(n) \) denote the smallest positive integer divisible by all of \( 2, 3, \ldots, n \). Find all prime numbers \( p, q \) such that \( q = p + 2 \) and \( L(q) > qL(p) \).

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