
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
$P$ is a moving point on the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$ in the first quadrant. Two tangent lines $PA$ and $PB$ are drawn from point $P$ to the circle $x^{2}+y^{2}=9$, touching the circle at points $A$ and $B$ respectively. The line $AB$ intersects the $x$-axis and $y$-axis at points $M$ and $N$. What is the minimum area of the triangle $MON$?

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