
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 $xOy$, curve $C_1$ is given by the parametric equations $\begin{cases} x=1+2t \\ y=2-2t \end{cases}$ (where $t$ is the parameter). With $O$ as the pole and the non-negative half-axis of the $x$-axis as the polar axis, the polar equation of curve $C_2$ is $\rho - \rho \cos^2 \theta - 2\cos \theta = 0$.  
(I) Convert the parametric equations of curve $C_1$ into a standard equation; convert the polar equation of curve $C_2$ into a Cartesian coordinate equation;  
(II) If point $P(1,2)$ and the intersection points of curve $C_1$ and $C_2$ are $A$ and $B$, find the value of $|PA| + |PB|$.

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