
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 the sum (or difference) of two numbers is the square of some number, then the doubled sum (or difference) of their cubes is the sum of the squares of three other numbers.

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