
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
a) For which integer values of \( k \) is the equality

\[ x^{2} + y^{2} + z^{2} = k \cdot x \cdot y \cdot z \]

possible, where \( x, y, z \) are positive integers?

b) Find all possible triples of integers within the first thousand such that the sum of their squares is divisible by their product.

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