
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
Find the standard equation and eccentricity of the conic section that satisfies the following conditions:  
(1) The ellipse has its foci on the y-axis and passes through the points (0,2) and (1,0).  
(2) The hyperbola has its foci at (0, ±6) and shares the same asymptotes with the hyperbola $-y^2 = 1$.

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