
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
Compute the sum of cubes of all even numbers from 2 to 100 inclusive, then add the sum of cubes of all negative versions of these numbers, and finally add 4 to each term in the original sequence of positive cubes. Thus, evaluate:
$$2^3 + 4^3 + 6^3 + ... + 100^3 \quad \text{and} \quad (-2)^3 + (-4)^3 + (-6)^3 + ... + (-100)^3,$$ 
then calculate the sum with adding 4 for each term in the even sequence:
$$(2^3 + 4) + (4^3 + 4) + (6^3 + 4) + ... + (100^3 + 4).$$

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