
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 that P is a moving point on the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{3}=1$, and through point P, two tangents are drawn to the circle $(x+1)^{2}+y^{2}=1$, with the points of tangency being A and B respectively, determine the range of values for $\overrightarrow{PA}\cdot \overrightarrow{PB}$.

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