
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 curve $C$: $x^{2}=8y$, with $F$ as the focus and point $P$ on the directrix, the line $PF$ intersects the curve $C$ at points $D$ and $E$.

(1) If $\overrightarrow{PF}=\overrightarrow{FE}$, and $E$ is in the first quadrant, find the equation of the line $PF$.
(2) Find the maximum value of $\overrightarrow{DP}\cdot\overrightarrow{PE}$, and find the coordinates of point $P$ at this time.

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