
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 $xOy$, the parametric equation of curve $C$ is $\begin{cases} & x=4\cos \theta, \\ & y=2\sin \theta \end{cases}$ (where $\theta$ is the parameter), and the parametric equation of line $l$ is $\begin{cases} & x=t+\sqrt{3}, \\ & y=2t-2\sqrt{3} \end{cases}$ (where $t$ is the parameter). Line $l$ intersects curve $C$ at points $A$ and $B$.

    (1) Find the value of $|AB|$;

    (2) If $F$ is the left focus of curve $C$, find the value of $\overrightarrow{FA} \cdot \overrightarrow{FB}$.

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