
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
Consider a sequence  $F_0=2$ ,  $F_1=3$  that has the property  $F_{n+1}F_{n-1}-F_n^2=(-1)^n\cdot2$ . If each term of the sequence can be written in the form  $a\cdot r_1^n+b\cdot r_2^n$ , what is the positive difference between  $r_1$  and  $r_2$ ?


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