
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
Tangents are drawn from the point \( P\left(\frac{3}{5}, \frac{14}{5}\right) \) to the ellipse \( 4 x^{2}+9 y^{2}=36 \). What are the equations of these tangents? Determine the equation and area of the circle that passes through the point and the points of tangency.

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