
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 Cartesian coordinate system, the parametric equation of curve \\(C\\) is given by \\(\begin{cases} x = \sqrt{5}\cos\varphi \\ y = \sqrt{15}\sin\varphi \end{cases}\\) (where \\(\varphi\\) is the parameter), and the parametric equation of line \\(l\\) is given by \\(\begin{cases} x = -\frac{1}{2}t \\ y = \sqrt{3} + \frac{\sqrt{3}}{2}t \end{cases}\\) (where \\(t\\) is the parameter). Establish a polar coordinate system with the origin as the pole and the positive half-axis of \\(x\\) as the polar axis. The polar coordinates of point \\(P\\) are \\((\sqrt{3}, \frac{\pi}{2})\\).
\\((\\)Ⅰ\\()\\) Find the Cartesian coordinates of point \\(P\\), and derive the general equation of curve \\(C\\);
\\((\\)Ⅱ\\()\\) Suppose the two intersection points of line \\(l\\) and curve \\(C\\) are \\(A\\) and \\(B\\), calculate the value of \\(|PA| + |PB|\\).

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