
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 ellipse $$C: \frac{x^2}{a^2} + y^2 = 1 (a > 1)$$, its top vertex is A, and its left and right foci are respectively F<sub>1</sub> and F<sub>2</sub>. The line AF<sub>2</sub> is tangent to the circle M: $x^2 + y^2 - 6x - 2y + 7 = 0$.
(Ⅰ) Find the equation of the ellipse;
(Ⅱ) If for a moving point P inside the ellipse C, $|PF_1|$, $|PO|$, $|PF_2|$ form a geometric sequence (where O is the origin), find the range of values for $\overrightarrow{PF_1} \cdot \overrightarrow{PF_2}$.

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