
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 how many pairs of positive integers \( (a, b) \) with \(a + b \leq 100\) satisfy the equation 
\[
\frac{a + b^{-1}}{a^{-1} + b} = 7
\]
A) 10
B) 11
C) 12
D) 13
E) 14

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