
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 \(a + b \leq 150\) satisfy the equation:
\[
\frac{a + 2b^{-1}}{a^{-1} + 2b} = 17
\]
A) 6   
B) 8   
C) 7   
D) 5

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