
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 $C\_1$ is $\begin{cases} x=1+ \frac{1}{2}t \
y=\frac{ \sqrt{3}}{2}t \end{cases}$ ($t$ is the parameter), and in the polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis, the curve $C\_2$ is: $ρ^{2}= \frac{12}{3+\sin ^{2}θ}$.

(1) Find the ordinary equation of curve $C\_1$ and the rectangular coordinate equation of $C_{2}$;
(2) If $C_{1}$ and $C_{2}$ intersect at points $A$ and $B$, and point $F(1,0)$, find the value of $\frac{1}{|FA|}+ \frac{1}{|FB|}$.

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