
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 an ellipse with a focal distance of 8 and a major axis length of 10, with the foci on the x-axis, find the standard equation of the ellipse.
2. Given a hyperbola C with its center at the origin and its right focus at F(3, 0), and an eccentricity of $\frac{3}{2}$, find the standard equation of the hyperbola.

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