
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
Consider the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$. A point $M$ on this ellipse is used to create two tangent lines to the circle $x^{2} + y^{2} = 2$. Let $A$ and $B$ be the points of tangency. If the line $l$ passing through $A$ and $B$ intersects the $x$-axis and $y$-axis at points $P$ and $Q$ respectively, find the minimum possible area of the triangle $POQ$.

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