
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
Given $p \gt 0$, $q \gt 0$, and satisfying $\log _{16}p=\log _{20}q=\log _{25}(p+q)$, find $\frac{p}{q}$.

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