
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
How many pairs of positive integers \((a, b)\) with \(a+b \leq 120\) satisfy the equation
\[\frac{a+2b^{-1}}{a^{-1}+2b} = 17?\]
- A) 3
- B) 4
- C) 5
- D) 6

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