
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 $c$ and $d$ be positive real numbers, with $c > 2d$. Compute the sum of the infinite series:
\[
\frac{1}{cd} + \frac{1}{c(3c - 2d)} + \frac{1}{(3c - 2d)(5c - 4d)} + \frac{1}{(5c - 4d)(7c - 6d)} + \dotsb.
\]

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