
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
Coordinate System and Parametric Equations.  
Given the curve $C$:  
$$
\begin{cases}
x=\cos \theta \\
y=\sin \theta
\end{cases}
(\theta \text{ is the parameter}).
$$

$(1)$ Convert the parametric equations of $C$ into a standard equation;  
$(2)$ If the coordinates of each point on $C$ undergo a scaling transformation $\begin{cases} x'=3x \\ y'=2y \end{cases}$ to obtain the curve $C'$, find the maximum value of the product of the distances from any point on $C'$ to the two coordinate axes.

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