
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
For a positive integer $n$, let
\[ H_n = 1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n} \]
Compute
\[ \sum_{n=1}^{100} \frac{n^2}{(n+1)H_nH_{n+1}} \]

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