
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 parametric equation of curve $C_1$ as 
$$
\begin{cases} 
x = 1 + \frac{1}{2}t \\
y = \frac{\sqrt{3}}{2}t 
\end{cases}
$$
($t$ is the parameter). In the polar coordinate system with the origin as the pole and the positive direction of the axis as the polar axis, the equation of curve $C_2$ is $\rho^2 = \frac{12}{3 + \sin^2\theta}$.

(Ⅰ) Find the general equation of curve $C_1$ and the rectangular coordinate equation of $C_2$;  
(Ⅱ) If $C_1$ and $C_2$ intersect at points $A$ and $B$, and let point $F(1,0)$, find the value of $\frac{1}{|FA|} + \frac{1}{|FB|}$.

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