
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 positive real numbers with $p>2q$. Compute 
\[ \frac{1}{pq} + \frac{1}{p(3p - 2q)} + \frac{1}{(3p - 2q)(5p - 4q)} + \frac{1}{(5p - 4q)(7p - 6q)} + \dotsb. \]

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