
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 that the polar equation of curve C is $$ρ^{2} = \frac{36}{4\cos^{2}θ + 9\sin^{2}θ}$$,  
(1) Taking the pole as the origin and the line of the polar axis as the x-axis, find the rectangular (Cartesian) coordinate equation of curve C;  
(2) If P(x, y) is a moving point on curve C, find the maximum value of 3x + 4y.

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