
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 $l$ passes through the right focus of the hyperbola $x^2 - y^2 = 1$ and intersects the hyperbola at points $A$ and $B$. If the real number $\lambda$ makes $|AB| = \lambda$ and there are exactly 3 such lines $l$, then $\lambda = \quad$.

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