
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 nonzero natural numbers \( a, b, c \) satisfy the equation \( a^{2} + b^{2} - c = 2022 \). Find:
(1) The minimum value of \( a^{2} + b^{2} + c^{2} \);
(2) The values of \( a, b, c \) when \( a^{2} + b^{2} + c^{2} \) reaches the minimum value.

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