
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
In the Cartesian coordinate system $(xOy)$, it is known that the line $l$: $\begin{cases} x=1+ \frac { \sqrt {3}}{2}t \\ y= \frac {1}{2}t \end{cases}(t$ is a parameter $)$ intersects the circle $C$: $\begin{cases} x=2+3\cos \theta \\ y=3\sin \theta \end{cases}(\theta$ is a parameter $)$ at points $A$ and $B$.
(1) Find the general equations for line $l$ and circle $C$.
(2) Given $F(1,0)$, find the value of $|FA|+|FB|$.

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