
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
Select Lecture on Coordinate System and Parametric Equations.  
Given the curve C: $$\begin{cases} x = \cos\theta \\ y = \sin\theta \end{cases}$$ (where $\theta$ is a parameter).
(1) Convert the parametric equations of curve C into a standard equation;
(2) If the coordinates of each point on curve C undergo a scaling transformation $$\begin{cases} x' = 3x \\ y' = 2y \end{cases}$$ the resulting curve is C'. Calculate the maximum value of the product of any point's distance to the two coordinate axes on curve C'.

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