
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
Through the right focus of the hyperbola \( x^{2} - \frac{y^{2}}{2} = 1 \), draw a line \( l \) that intersects the hyperbola at points \( A \) and \( B \). If there are exactly 3 lines \( l \) such that \( |AB| = \lambda \), determine the value of \( \lambda \).

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