
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, given the circle \\(O: \cos \theta + \sin \theta\\) and the line \\(\rho \sin (\theta - \frac{\pi}{4}) = \frac{\sqrt{2}}{2}\\).
\\((1)\\) Find the Cartesian coordinate equations of circle \\(O\\) and line \\(l\\);
\\((2)\\) When \\(\theta \in (0,\pi)\\), find the polar coordinates of the intersection points of line \\(l\\) and circle \\(O\\).

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