
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 line $l: y=kx+1\left(k \gt 0\right)$ passes through the focus $F$ of the parabola $C: x^{2}=2py$, and $l$ intersects $C$ at points $A$ and $B$, and the directrix of $C$ at point $E$. If $\overrightarrow{EF}=\overrightarrow{FB}$, then $p=$____, $k=$____.

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