
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 \( p \) and \( q \) be real numbers such that 
\[ \frac{p}{q} + \frac{p}{q^2} + \frac{p}{q^3} + \dots = 5. \]
Find 
\[ \frac{p}{p^2 + q} + \frac{p}{(p^2 + q)^2} + \frac{p}{(p^2 + q)^3} + \dots. \]

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