
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 the hyperbola $\dfrac {x^{2}}{4}- \dfrac {y^{2}}{b^{2}}=1(b > 0)$ with eccentricity $\dfrac { \sqrt {5}}{2}$, where $F_{1}$ and $F_{2}$ are the two foci of the hyperbola, $A$ is the left vertex, and $B(0,b)$, if point $P$ is on the line segment $AB$, then the minimum value of $\overrightarrow{PF_{1}}\cdot \overrightarrow{PF_{2}}$ is ______.

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