
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 right focus of the ellipse is $F\left(m,0\right)$, the left and right directrices are $l_{1}:x=-m-1$, $l_{2}:x=m+1$, and $l_{1}$, $l_{2}$ intersect the line $y=x$ at points $A$, $B$.

(1) If the eccentricity is $\dfrac{\sqrt {2}}{2}$, find the equation of the ellipse.

(2) When $\overrightarrow {AF}\cdot \overrightarrow {FB} \lt 7$, find the range of eccentricity of the ellipse.

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