
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 $C\_1$ is given by $x=cos⁡θ, y=sin⁡θ$, where $θ$ is the parameter. By stretching the horizontal coordinates of all points on curve $C\_1$ to twice their original length and the vertical coordinates to $√3$ times their original length, we obtain curve $C\_2$.
(I) Find the general equation of curve $C\_2$;
(II) Given point $B(1,1)$, curve $C\_2$ intersects the negative semi-axis of $x$ at point $A$. $P$ is any point on curve $C\_2$. Find the maximum value of $|PA|^2-|PB|^2$.

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