
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 \( x, y, z \) such that
\[ n = x^3 + y^3 + z^3 - 3xyz, \]
then \( n \) is said to have property \( P \).

(1) Determine whether \( 1, 2, 3 \) have property \( P \).

(2) Among the 2014 consecutive integers from \( 1 \) to \( 2014 \), how many do not have property \( P \)?

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