
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
Suppose \( a \) and \( b \) are positive numbers such that \(\log_8(a) = \log_{18}(b) = \log_{32}(a+b)\). Determine the value of \( \frac{b}{a} \).
A) \( \frac{4}{3} \)
B) \( \frac{1+\sqrt{3}}{2} \)
C) \( \frac{1+\sqrt{5}}{2} \)
D) \( \frac{3 + 2\frac{\log 3}{\log 2}}{1 + 2\frac{\log 3}{\log 2} + 5} \)
E) \( \frac{16}{9} \)

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