
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 Cartesian coordinate system $(xOy)$, with the origin as the pole and the positive semi-axis of $x$ as the polar axis, a curve $C$ has the polar equation $ρ^2 - 4ρ\sin⁡θ + 3 = 0$. Points $A$ and $B$ have polar coordinates $(1,π)$ and $(1,0)$, respectively.
(1) Find the parametric equation of curve $C$;
(2) Take a point $P$ on curve $C$ and find the maximum and minimum values of $|AP|^2 + |BP|^2$.

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