
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  $\{a_{n}\}_{n \geq 0}$  and  $\{b_{n}\}_{n \geq 0}$  be two sequences of integer numbers such that:

i.  $a_{0}=0$ ,  $b_{0}=8$ .

ii. For every  $n \geq 0$ ,  $a_{n+2}=2a_{n+1}-a_{n}+2$ ,  $b_{n+2}=2b_{n+1}-b_{n}$ .

iii.  $a_{n}^{2}+b_{n}^{2}$  is a perfect square for every  $n \geq 0$ .

Find at least two values of the pair  $(a_{1992},\, b_{1992})$ .

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