
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 \\(O\\) as the polar axis, a polar coordinate system is established. The polar equation of curve \\(C\\) is \\(\rho=2(\sin \theta+\cos \theta+ \frac {1}{\rho}).\\)  
\\((1)\\) Write the parametric equation of curve \\(C\\);  
\\((2)\\) Take any point \\(P\\) on curve \\(C\\), and draw perpendiculars to the \\(x\\)-axis and \\(y\\)-axis through point \\(P\\), with the feet of the perpendiculars being \\(A\\) and \\(B\\) respectively. Find the maximum value of the area of rectangle \\(OAPB\\).

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