
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
Given matrix A= $$\begin{bmatrix} 2 & 0 \\ 1 & k\end{bmatrix}$$, which has a characteristic vector of $$\overrightarrow {α}$$\= $$\begin{bmatrix} \overset{-1}{1}\end{bmatrix}$$ corresponding to the characteristic value λ.

(1) Find the real number k and the value of λ.
(2) If curve C is transformed into curve C' with the corresponding matrix A transformation, and the equation of curve C' is x<sup>2</sup>+y<sup>2</sup>\=2, find the equation of curve C.

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