
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 $(xOy)$, the equation of curve $C$ is $y=3+ \sqrt {-x^{2}+8x-15}$.
(1) Write a parametric equation of curve $C$;
(2) Take a point $P$ on curve $C$, draw perpendiculars from point $P$ to the $x$-axis and $y$-axis, with the feet of the perpendiculars being $A$ and $B$ respectively. Find the range of values for the perimeter of rectangle $OAPB$.

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