
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
The left focus and the line vertical to the $x$-axis of the hyperbola $\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}=1(a > 0,b > 0)$ intersect with the hyperbola at points $M$ and $N$. A circle with $MN$ as its diameter passes through the right vertex of the hyperbola. What is the eccentricity of the hyperbola?

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