
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 \( t_n = \frac{n(n+2)}{2} \) (where a small change has been made in the formula of the triangular number). Calculate the sum:
\[ \frac{1}{t_1} + \frac{1}{t_2} + \frac{1}{t_3} + \ldots + \frac{1}{t_{1002}} \]
A) $\frac{1506}{1003}$
B) $\frac{1507}{1004}$
C) $\frac{1508}{1005}$
D) $\frac{1509}{1006}$

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