
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
Given the parametric equations of curve $C$ as $\begin{cases} x=3\cos \theta \\ y=2\sin \theta \end{cases}$ ($\theta$ is the parameter), a coordinate transformation $\begin{cases} x'=\frac{1}{3}x \\ y'=\frac{1}{2}y \end{cases}$ is applied to points on curve $C$ to obtain curve $C'$.

(1) Find the Cartesian equation of curve $C'$.

(2) If point $A$ is on curve $C'$, and point $B(3,0)$, find the trajectory equation of the midpoint $P$ of $AB$ as point $A$ moves along curve $C'$.

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