
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
Let $A,B$ be two different points on the same asymptote of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=\lambda (\lambda \ne 0)$, with $\overrightarrow{m}=(1,0)$, $|\overrightarrow{AB}|=6$, $\frac{\overrightarrow{AB}\cdot \overrightarrow{m}}{|\overrightarrow{m}|}=3$. Then, the eccentricity of the hyperbola is ______________.

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