
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
If
\[1 \cdot (1 + 1) \cdot 1001 + 2 \cdot (1001 - 1) \cdot (2 + 1) + 3 \cdot (1001 - 2) \cdot (3 + 1) + \dots + 1000 \cdot 1 \cdot 1001 = 1001 \cdot 500.5 \cdot y,\]
compute the integer \(y\).

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