
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
From a point \( M \) on the ellipse \(\frac{x^{2}}{9}+\frac{y^{2}}{4}=1\), two tangent lines are drawn to the circle with the minor axis of the ellipse as its diameter. The points of tangency are \( A \) and \( B \). The line \( AB \) intersects the \(x\)-axis and \(y\)-axis at points \( P \) and \( Q \) respectively. Find the minimum value of \(|PQ|\).

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