
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 $a$, $b$, and $c$ be positive real numbers, with $a > b > c$. Compute
\[
\frac{1}{bc} + \frac{1}{c(2c - a)} + \frac{1}{(2c - a)(3c - 2b)} + \frac{1}{(3c - 2b)(4c - 3a)} + \dotsb.
\]

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