
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 $l: 
\begin{cases}
x = 1 + \dfrac{\sqrt{2}}{2}t \\
y = \dfrac{\sqrt{2}}{2}t
\end{cases} (t$ is the parameter), and the curve $C_1: 
\begin{cases}
x = 2\cos\theta \\
y = \sqrt{3}\sin\theta
\end{cases} (\theta$ is the parameter)
1. Find the general equation of line $l$ and curve $C_1$.
2. Given points $F(1,0)$ and $F_1(-1,0)$, if line $l$ intersects with curve $C_1$ at points $A$ and $B$ (with point $A$ above point $B$), find the value of $|F_1A| - |F_1B|$.

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