
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
Given an ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$ and a point $M(3, 2)$ inside the ellipse, a line $AB$ intersects the ellipse at points $A$ and $B$. Another line $CD$ intersects the ellipse at points $C$ and $D$. Tangent lines to the ellipse are drawn at points $A$ and $B$ and intersect at point $P$. Similarly, tangent lines to the ellipse are drawn at points $C$ and $D$ and intersect at point $Q$. Find the equation of the line passing through points $P$ and $Q$.

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