
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 such that
\[
\frac{a}{b} + \frac{2a+5b}{b+5a} = 4.
\]
Find $\frac{a}{b}.$ (Set $b = 1$ for simplification.)
A) $\frac{18 + \sqrt{258}}{8}$
B) $\frac{17 + \sqrt{269}}{10}$
C) $\frac{16 + \sqrt{280}}{10}$
D) $\frac{15 + \sqrt{275}}{12}$

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