
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
Let $P$ be any point on the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (a>b>0)$. $P_{1} P_{2}$ is any chord of the ellipse. The slopes of the lines $P P_{1}$ and $P P_{2}$ are $k_{1}$ and $k_{2}$, respectively. If the chord $P_{1} P_{2}$ passes through the center $O$, then $k_{1} \cdot k_{2}=-\frac{b^{2}}{a^{2}}$.

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