
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 equations of curve $C_1$ as
\[
\begin{cases} 
& x=1+\frac{1}{2}t \\
& y=\frac{\sqrt{3}}{2}t 
\end{cases}
\]
(where $t$ is the parameter). In the polar coordinate system with the origin as the pole and the positive half-axis of $x$ 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 Cartesian coordinate equation of $C_2$;

(Ⅱ) If $C_1$ intersects $C_2$ at points $A$ and $B$, and given point $F(1,0)$, find the value of $\frac{1}{|AF|}+\frac{1}{|BF|}$.

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