
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) The vertex of an ellipse, whose foci are on the x-axis, is A(2,0). The length of the major axis is twice that of the minor axis. Find the standard equation of the ellipse.

(2) One asymptote of a hyperbola is given by the equation x + 2y = 0, and it passes through the point (2,2). Find the standard equation of this hyperbola.

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