
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 that \( p \) and \( q \) are positive numbers for which
\[
\log_{8}(p) = \log_{18}(q) = \log_{32}(p+q).
\]
Determine the value of \(\frac{q}{p}\).
A) \(\frac{4}{3}\) \\
B) \(\frac{1+\sqrt{3}}{2}\) \\
C) \(\frac{8}{5}\) \\
D) \(\frac{1+\sqrt{5}}{2}\) \\
E) \(\frac{16}{9}\)

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