
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
In the hyperbola $\dfrac {x^{2}}{a^{2}} - \dfrac {y^{2}}{b^{2}} = 1$ ($a,b > 0$), if a line with a slope of $1$ passing through the left vertex $A$ of the hyperbola intersects the right branch at point $B$, and the projection of point $B$ on the $x$-axis is exactly the right focus $F$ of the hyperbola, then the eccentricity of this hyperbola is ______.

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