
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 line \( l \) passes through the left focus \( F \) of the ellipse \( C: \frac{x^{2}}{2} + y^{2} = 1 \) and intersects the ellipse \( C \) at points \( A \) and \( B \). Let \( O \) be the origin. If \( O A \) is perpendicular to \( O B \), find the distance from the point \( O \) to the line \( A B \).

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