
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 a line \( l \) passing through the left focus \( F \) of the ellipse \( C: \frac{x^2}{2} + y^2 = 1 \) and intersecting the ellipse \( C \) at points \( A \) and \( B \), where \( O \) is the origin. If \( OA \perp OB \), find the distance from \( O \) to the line \( AB \).

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