
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
Let $a$ and $b$ be distinct real numbers for which:
\[
\frac{a}{b} + \frac{3a + 4b}{b + 12a} = 2.
\]
Find $\frac{a}{b}$.
A) $\frac{5 + \sqrt{19}}{6}$ 
B) $\frac{5 - \sqrt{19}}{6}$ 
C) $0.8$ 
D) $0.5$

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