
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 $B$ be the set of positive integers that have no prime factors other than $2$, $3$, $5$, or $7$. The infinite sum of the reciprocals of the elements of $B$ can be expressed as $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. What is $p+q$?
A) 37
B) 41
C) 43
D) 45
E) 47

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