
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 rectangular coordinate system $(xOy)$, line $l$ passes through point $P(2,6)$ with a slope angle of $\frac{3}{4}\pi$. In the polar coordinate system, which has the same length as the rectangular coordinate system $(xOy)$, takes the origin $O$ as the pole, and the non-negative semi-axis of the $x$-axis as the polar axis, the polar equation of curve $C$ is $\rho =20\sin (\frac{\pi }{4}-\frac{\theta }{2})\cos (\frac{\pi }{4}-\frac{\theta }{2})$.

(I) Find the parametric equation of line $l$ and the Cartesian equation of curve $C$;

(II) Suppose curve $C$ intersects line $l$ at points $A$ and $B$, find $|PA|+|PB|$.

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