
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 origin O as the pole and the positive half-axis of the x-axis as the polar axis, a polar coordinate system is established. The polar equation of curve C is given by $$\rho=2(\sin\theta+\cos\theta+ \frac {1}{\rho})$$.
(1) Find the parametric equation of curve C;
(2) For any point P(x, y) on curve C, find the maximum value of $3x+4y$.

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