
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
Let \( n \) be an integer. If there exist integers \( x \), \( y \), and \( z \) such that \( n = x^3 + y^3 + z^3 - 3xyz \), then \( n \) is said to have property \( P \).

Among the numbers 1, 5, 2013, and 2014, which ones have property \( P \) and which ones do not? Provide reasons.

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