
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
Evaluate the sum of the reciprocals of the first 1000 triangular numbers:
\[ \frac{1}{t_1} + \frac{1}{t_2} + \frac{1}{t_3} + \ldots + \frac{1}{t_{1000}} \]
where $t_n$ is defined as the $n$-th triangular number, $t_n = \frac{n(n+1)}{2}$.
A) $\frac{2000}{1001}$  
B) $\frac{1000}{501}$  
C) $\frac{3000}{1501}$  
D) $2$

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