
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 polar coordinate system, the equation of curve $C$ is given by $({{\rho }^{2}}=\dfrac{3}{1+2{{\sin }^{2}}\theta })$, and point $R$ is $(2\sqrt{2},\dfrac{\pi }{4})$.

(1) Establish a rectangular coordinate system with the pole as the origin and the positive half of the $x$-axis as the polar axis. Convert the polar coordinate equation of curve $C$ to a rectangular coordinate equation and the polar coordinates of point $R$ to rectangular coordinates.

(2) Let $P$ be a moving point on curve $C$. The rectangle $PQRS$ has diagonal $PR$ and one side perpendicular to the polar axis. Find the minimum value of the perimeter of rectangle $PQRS$ and the rectangular coordinates of point $P$ at this time.

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