
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
Five integers form an arithmetic sequence. Whether we take the sum of the cubes of the first four terms, or the sum of the cubes of the last four terms, in both cases, we obtain 16 times the square of the sum of the considered terms. Determine the numbers.

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