
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
Calculate the summation:
\[
\sum_{n=1}^{2500} \frac{1}{\frac{n(n+1)}{2}}
\]
where $\frac{n(n+1)}{2}$ denotes the $n$th triangular number.
A) $\frac{5002}{2501}$
B) $\frac{5000}{2501}$
C) $\frac{4999}{2500}$
D) $\frac{5001}{2502}$

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