
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
What is the difference between the sum of the squares of the first $1001$ odd counting numbers and the sum of the cubes of the first $1001$ even counting numbers?
A) -1000000000
B) -799700002
C) -500000000
D) 1004006001
E) 2002003003

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