
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
A line \( l \) passing through the origin \( O \) intersects the ellipse \( C: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) (\( a > b > 0 \)) at points \( M \) and \( N \). Let \( P \) be any point on the ellipse \( C \) other than \( M \) and \( N \). If the product of the slopes of the lines \( PM \) and \( PN \) is \( -\frac{1}{3} \), determine the eccentricity of the ellipse \( C \).

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