
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
If point $P_{0}(x_{0},y_{0})$ is outside the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ $(a > b > 0)$, and two tangents to the ellipse are drawn from $P_{0}$, touching the ellipse at points $P_{1}$ and $P_{2}$, then the equation of the line containing the chord $P_{1}P_{2}$ is $\frac{x_{0}x}{a^{2}}+\frac{y_{0}y}{b^{2}}=1$. Similarly, for the hyperbola $\frac{x^{2}}{a^{2}}- \frac{y^{2}}{b^{2}}=1$ $(a > 0,b > 0)$, a correct proposition can be stated as "If point $P_{0}(x_{0},y_{0})$ is not on the hyperbola $\frac{x^{2}}{a^{2}}- \frac{y^{2}}{b^{2}}=1$ $(a > 0,b > 0)$, and two tangents to the hyperbola are drawn from $P_{0}$, touching the hyperbola at points $P_{1}$ and $P_{2}$, then the equation of the line containing the chord $P_{1}P_{2}$ is ______."

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