
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
(1) Given that the axes of symmetry of an ellipse are the coordinate axes, the sum of the lengths of the major axis and minor axis is 18, and the focal length is 6, find the equation of the ellipse;
(2) Find the equation of the hyperbola that shares the same foci with the ellipse $\frac{x^{2}}{4}+y^{2}=1$ and passes through point Q(2,1).

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