
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 the line $y=kx+m$ intersects the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1 (a>0, b>0)$ at points $A$ and $B$ where the two asymptotes of the hyperbola intersect, and intersects the line $y=\frac{1}{k}x$ at point $N$, if $N$ is the midpoint of $AB$, then the eccentricity of the hyperbola is ____.

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