
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 the hyperbola C: $$\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}$$\=1 (a>0, b>0), its asymptotes intersect with the circle (x-2)<sup>2</sup>+y<sup>2</sup>\=2, and the length of both chords formed by the intersection of the asymptotes and the circle is 2. Find the eccentricity of the hyperbola.

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