
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
Given that point P is a point on the right side of the y-axis of the ellipse $\frac{x^{2}}{5} + \frac{y^{2}}{4} = 1$, and the area of the triangle with point P and foci $F_1$ and $F_2$ as vertices is equal to 1, find the coordinates of point P.

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