
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 $F$ is the focus of the hyperbola $\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1(a＞0,b＞0)$, $B$ is an endpoint of the imaginary axis, and the line segment $BF$ intersects the hyperbola at point $M$, where point $M$ is exactly the midpoint of the line segment $BF$. Find the eccentricity of the hyperbola.

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