
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
In the polar coordinate system, curve C: $\rho=2\cos\theta$, line l: $\rho\cos(\theta- \frac{\pi}{3})= \frac{3}{2}$.  
(1) Find the rectangular coordinate equations for curve C and line l;  
(2) O is the pole, A and B are two points on curve C, and $\angle AOB= \frac{\pi}{3}$, find the maximum value of $|OA|+|OB|$.

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