
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
Consider the set $B$ of positive integers that have no prime factors other than $2$, $3$, $5$, or $7$. Calculate the infinite sum of the reciprocals of the elements of $B$. Express the result as a fraction $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers, and find $p+q$.
A) 40
B) 42
C) 43
D) 45
E) 48

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