
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 on a plane, the slope angle of line $l$ passing through point $M(2,1)$ is $\frac{\pi }{4}$. Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of the $x$-axis as the polar axis, using the same length unit as the rectangular coordinate system. For the curve $C:\\rho =4\\sqrt{2}\\sin (\\theta +\\frac{\pi }{4})$,

(I) Find the parametric equation of line $l$ and the rectangular coordinate equation of curve $C$.

(II) If line $l$ intersects curve $C$ at points $A$ and $B$, find the value of $\frac{1}{|MA|}+\\dfrac{1}{|MB|}$.

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