
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
Through any point P on the hyperbola $\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}=1(a > 0,b > 0)$, draw a line parallel to the y-axis, intersecting the two asymptotes at points A and B. If $\overrightarrow{PA}\cdot \overrightarrow{PB}=- \frac {a^{2}}{4}$, determine the eccentricity of the hyperbola.

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