
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 that the ellipse $C$ has two foci $F\_1(-1,0)$, $F\_2(1,0)$, and passes through the point $E(\sqrt{3},\frac{\sqrt{3}}{2})$.

(1) Find the standard equation of the ellipse $C$ ;

(2) The line $l$ passing through point $F\_1$ intersects the ellipse $C$ at points $A$ and $B$ (with point $A$ located above the $x$-axis), and $\overrightarrow{AF_{1}}=λ\overrightarrow{F_{1}B}$, with $2≤slant λ < 3$, find the range of the slope $k$ of line $l$.

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