
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 equations of the conic sections satisfying the following conditions:
1. An ellipse that passes through the point $(-3, 2)$ and has the same foci as the ellipse defined by $\frac{x^2}{9} + \frac{y^2}{4} = 1$;
2. A parabola with the origin as the vertex, the coordinate axes as the axes of symmetry, and passes through the point $P(-4, -4\sqrt{2})$.

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