
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
Convert the following second-order equations to their canonical form:

1) \(8 x^{2}+4 x y+5 y^{2}-56 x-32 y+80=0\);
2) \(3 x^{2}+10 x y+3 y^{2}-2 x-14 y-13=0\);
3) \(x^{2}-4 x y+4 y^{2}-2 x-6 y+2=0\);
4) \(x^{2}+y^{2}-3 x+2 y=0\);
5) \(3 x^{2}-4 x y+3 y^{2}+20=0\).

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