
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 line \\(l:\\begin{cases} & x=1+\\dfrac{\\sqrt{2}}{2}t \\\\ & y=\\dfrac{\\sqrt{2}}{2}t \\end{cases}\\) (where \\(t\\) is a parameter), and the curve \\({{C}\_{1}}:\\begin{cases} & x=2\\cos \\theta \\\\ & y=\\sqrt{3}\\sin \\theta \\end{cases}\\) (where \\(\\theta\\) is a parameter).

\\((1)\\) Find the general equation of line \\(l\\) and curve \\({{C}\_{1}}\\).

\\((2)\\) Given points \\(F(1,0)\\), \\({{F}\_{1}}(-1,0)\\), if line \\(l\\) intersects curve \\({{C}\_{1}}\\) at points \\(A\\) and \\(B\\) (with point \\(A\\) above point \\(B\\)), find the value of \\(|{{F}\_{1}}A|-|{{F}\_{1}}B|\\).

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