
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
Taking the origin \\(O\\) of the Cartesian coordinate system as the pole and the positive half-axis of the \\(x\\)-axis as the polar axis, with both coordinate systems having equal units of measurement, it is known that line \\(l\\) passes through point \\(P(1,1)\\) with an inclination angle \\(\alpha = \dfrac{\pi}{6}\\).

\\((1)\\) Write the parametric equation of line \\(l\\).

\\((2)\\) Suppose \\(l\\) intersects the circle \\(\rho = 2\\) at two points \\(A\\) and \\(B\\). Find the product of the distances from point \\(P\\) to points \\(A\\) and \\(B\\).

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