
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 \( a_n \) and \( b_n \) be two sequences of integers such that:
1. \( a_0 = 0 \), \( b_0 = 8 \);
2. \( a_{n+2} = 2a_{n+1} - a_n + 2 \), \( b_{n+2} = 2b_{n+1} - b_n \);
3. \( a_n^2 + b_n^2 \) is a square for \( n > 0 \).

Find at least two possible values for \( (a_{1992}, b_{1992}) \).

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