
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 an ellipse $C: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ with eccentricity $\frac{\sqrt{3}}{2}$, and point $(2,0)$ lies on ellipse $C$.

(Ⅰ) Find the standard equation of ellipse $C$;  
(Ⅱ) A line passing through point $P(1,0)$ (not perpendicular to the coordinate axes) intersects the ellipse at points $A$ and $B$. Let point $B'$ be the reflection of point $B$ across the $x$-axis. Is the intersection point $Q$ of line $AB'$ and the $x$-axis a fixed point? Please explain your reasoning.

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