
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. Find the standard equation of an ellipse with a major axis length of 20 and an eccentricity of $\frac{3}{5}$.
2. Given that point P is on the ellipse $\frac{x^2}{5} + \frac{y^2}{4} = 1$, and the area of the triangle formed by point P and the foci $F_1$, $F_2$ is equal to 1, find the coordinates of point P.

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