
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 $$\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}} = 1$$ (0 < a < b) has a real axis length of 4, and the chord length cut by the line y = x - 2 is 20$$\sqrt {2}$$. Find:  
(1) The equation of the hyperbola;  
(2) The equation of the asymptotes.

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