
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 $c > d.$ Compute
\[\frac{1}{cd} + \frac{1}{c(2c - d)} + \frac{1}{(2c - d)(3c - 2d)} + \frac{1}{(3c - 2d)(4c - 3d)} + \dotsb.\]

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