
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
In the Cartesian coordinate system \(xOy\), the parametric equations for curve \(C_1\) are given by \(\begin{cases}x=1+2t \\ y=2-2t\end{cases} (t\) is the parameter), with \(O\) as the pole and the non-negative half of the \(x\)-axis as the polar axis, the polar equation for curve \(C_2\) is: \(\rho= \dfrac{2\cos θ}{\sin^2 \theta}\).

(Ⅰ) Express the equations for curve \(C_1\) as an ordinary equation; convert the equation for curve \(C_2\) to a Cartesian coordinate equation;
(Ⅱ) If point \(P(1,2)\), and points \(A\) and \(B\) are the intersections of curves \(C_1\) and \(C_2\), find the value of \(|PA|+|PB|\).

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