
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 in the Cartesian coordinate system, the curve \\(C\\): \\(x^{2}+y^{2}-6x-8y=0\\), line \\(l_{1}: x- \sqrt {3}y=0\\), and line \\(l_{2}: \sqrt {3}x-y=0\\). With the origin \\(O\\) as the pole and the positive half of the \\(x\\)-axis as the polar axis, a polar coordinate system is established.  
\\((1)\\) Write the parametric equation of curve \\(C\\) and the polar equations of lines \\(l_{1}\\) and \\(l_{2}\\);  
\\((2)\\) If line \\(l_{1}\\) intersects curve \\(C\\) at points \\(O\\) and \\(A\\), and line \\(l_{2}\\) intersects curve \\(C\\) at points \\(O\\) and \\(B\\), find the area of \\(\triangle AOB\\).

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