
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
Let \( P \) be a moving point on the ellipse \(\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1\) in the first quadrant. From point \( P \), two tangents \( PA \) and \( PB \) are drawn to the circle \( x^{2} + y^{2} = 9 \), with points of tangency \( A \) and \( B \) respectively. The line \( AB \) intersects the \( x \)-axis and \( y \)-axis at points \( M \) and \( N \) respectively. Find the minimum area of \( \triangle MON \).

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