
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
Evaluate the following expression: 
$$1^3 + 2^3 + 3^3 + \dots + 50^3 + 51^3$$
and 
$$(-1)^3 + (-2)^3 + (-3)^3 + \dots + (-50)^3 + (-51)^3$$ 
Compute their total sum and then subtract the sum of the first 51 even numbers squared.

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