
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 that point \( P\left(x_{0}, y_{0}\right) \) is not on the conic section \(\Gamma\):
$$
A x^{2} + B x y + C y^{2} + D x + E y + F = 0
$$

Two tangents can be drawn to \(\Gamma\) from point \( P \). Find the equation of the line passing through the points of tangency:
$$
\begin{array}{l}
2 A x_{0} x + B\left(x_{0} y + x y_{0}\right) + 2 C y_{0} y + \\
D\left(x_{0} + x\right) + E\left(y_{0} + y\right) + 2 F = 0.
\end{array}
$$

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