
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
Consider that \( y_1+2=y_2+3=y_3+4=\cdots=y_{1004}+1005=y_1+y_2+y_3+\cdots+y_{1004}+1006 \). 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