
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 \(y_1+1=y_2+2=y_3+3=\cdots=y_{1004}+1004=y_1+y_2+y_3+\cdots+y_{1004}+1005\). Find the value of \(\left\lfloor|T|\right\rfloor\), where \(T=\sum_{n=1}^{1004}y_n\).

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