
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 length of the major axis of an ellipse is $12 \mathrm{~cm}$, and the minor axis is $10 \mathrm{~cm}$. If we use the major axis as the x-axis and one of its vertices as the origin, find the abscissa corresponding to an ordinate of $4 \mathrm{~cm}$. Additionally, determine the equation of the tangent to the ellipse at the endpoint of the positive ordinate, its angle of inclination, and the area of the triangle formed by the axes and the tangent.

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