
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 parabola $E$: $y^{2}=4x$ with its focus $F$, and a line $l$ passing through point $F$ intersecting the parabola $E$ at points $A$ and $B$. Let $O$ be the origin.
(I) If the slope of line $l$ is $1$, find the value of $\overrightarrow{OA}\cdot \overrightarrow{OB}$;
(II) Assume $\overrightarrow{FB}=t \overrightarrow{AF}$, where $t\in[2,4]$. Determine the possible range of the slope of line $l$.

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