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

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