
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
In the Cartesian coordinate plane, it is not difficult to obtain "For any point $P$ on the hyperbola $xy=k (k>0)$, if the projections of point $P$ on the $x$-axis and $y$-axis are $E$ and $F$ respectively, then $|PE| \cdot |PF|$ must be a constant value $k$". Similarly, in the Cartesian coordinate plane, for any point $P$ on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1 (a>0, b>0)$, if [the projections of point $P$ on the asymptotes are $E$ and $F$ respectively], then [the product of the distances from point $P$ to the asymptotes is a constant value].

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