
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
\[
\frac{1}{ba^2} + \frac{1}{a^2(2a^2 - b^2)} + \frac{1}{(2a^2 - b^2)(3a^2 - 2b^2)} + \frac{1}{(3a^2 - 2b^2)(4a^2 - 3b^2)} + \dotsb.
\]

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