
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
On the ellipse $\frac {x^{2}}{4}+ \frac {y^{2}}{3}=1$, there is a moving point $P$. For the circle $E: (x-1)^{2}+y^{2}=1$, any line passing through the center of circle $E$ intersects the circle at points $A$ and $B$. For the circle $F: (x+1)^{2}+y^{2}=1$, any line passing through the center intersects the circle at points $C$ and $D$. The minimum value of $\overrightarrow{PA}\cdot \overrightarrow{PB}+ \overrightarrow{PC}\cdot \overrightarrow{PD}$ is \_\_\_\_\_\_.

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