
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) satisfy the equation
\[\frac{a+3b^{-1}}{a^{-1}+3b} = 7?\]
and also satisfy that $a + b \leq 150$?
A) 4
B) 5
C) 6
D) 7
E) 8

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