
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
(1) Are there any integer solutions $x$ and $y$ that satisfy the equation $x^2 - y^2 = 1998$? If yes, find the solutions; if no, explain why.  
(2) If the vertices of a cube are labeled with +1 or -1, and each face is labeled with a number equal to the product of the numbers at its four vertices, can the sum of the 14 labeled numbers be 0?

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