
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
The equation of an ellipse is $\left(\frac{x}{5}\right)^{2}+\left(\frac{y}{3}\right)^{2}=1$. At the right focus of this ellipse, we draw the positive ordinate and construct the tangent at its endpoint to the ellipse. What is the area of the triangle formed by this tangent line and the two coordinate axes?

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