
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 positive real numbers \( a \) and \( b \) (where \( a > b \)), what is the product of the distances from the points \(\left(\sqrt{a^{2}-b^{2}}, 0\right)\) and \(\left(-\sqrt{a^{2}-b^{2}}, 0\right)\) to the line
\[
\frac{x \cos \theta}{a}+\frac{y \sin \theta}{b}=1
\]

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