
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. An ellipse has an eccentricity of $\frac{1}{2}$, with foci at $(-3, 0)$ and $(3, 0)$. Find the equation of this ellipse.
2. A hyperbola has its foci on the x-axis, with $c=6$, and passes through point $A(-5, 2)$. Find the standard equation of this hyperbola.

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