
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 $(xOy)$, the parametric equation of line $l$ is $\begin{cases} & x=1+\frac{\sqrt{2}}{2}t \\ & y=-1+\frac{\sqrt{2}}{2}t \end{cases}$ ($t$ is the parameter). Establish a polar coordinate system with the origin as the pole and the positive half of the $x$-axis as the polar axis, using the same unit length in both coordinate systems. The polar equation of curve $C$ is $({\rho }^{2}+5=6\rho \mathrm{cos} \theta )$. Let $M$ and $N$ be the intersection points of line $l$ and curve $C$.

(I) Find the rectangular equation of curve $C$;

(II) Let $P$ be the intersection point of line $l$ and the ray $\theta =-\frac{\pi }{4}(\rho \ge 0)$. Calculate the value of $|PM|+|PN|$.

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