
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
Consider the hyperbola $M$: $x^{2}- \frac{y^{2}}{b^{2}}=1$. A line $l$ with a slope of $1$ is drawn from the left vertex $A$ of the hyperbola $M$. If $l$ intersects the two asymptotes of the hyperbola $M$ at points $B$ and $C$ respectively, and $|AB|=|BC|$, then calculate the eccentricity of the hyperbola $M$.

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