
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
Suppose that $y_1+2=y_2+4=y_3+6=\cdots=y_{1500}+3000=y_1+y_2+y_3+\cdots+y_{1500}+1501$. Find the value of $\left\lfloor|T|\right\rfloor$, where $T=\sum_{n=1}^{1500}y_n$.

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