
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
The parametric equation of curve C<sub>1</sub> is
$$
\begin{cases}
x=\cosθ \\
y=\sinθ
\end{cases}
$$
(where $θ$ is the parameter). By stretching the x-coordinates of all points on curve C<sub>1</sub> to twice their original length and the y-coordinates to $\sqrt{3}$ times their original length, we obtain curve C<sub>2</sub>.

(Ⅰ) Find the Cartesian equation of curve C<sub>2</sub>;

(Ⅱ) Given the point B(1,1), curve C<sub>2</sub> intersects the negative x-axis at point A. For any point P on curve C<sub>2</sub>, find the maximum value of $|PA|^2 - |PB|^2$.

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