
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 \(a\) and \(b\) be positive real numbers, with \(a > b\). Compute the series
\[
\frac{1}{a^2b} + \frac{1}{a^2(3a-b)} + \frac{1}{(3a-b)(5a-2b)} + \frac{1}{(5a-2b)(7a-3b)} + \dotsb.
\]

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