
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 a polar coordinate system with the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis, the polar equation of the curve $C$ is $ρ = 2( \sin θ + \cos θ + \frac{3}{2} ).$

(I) Find the parametric equations of the curve $C$;

(II) For any point $P(x, y)$ on the curve $C$, find the maximum value of $3x + 4y$.

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