
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 point $P$ is a moving point on the $y$-axis, point $M$ is a moving point on the $x$-axis, point $F(1,0)$ is a fixed point, and they satisfy $\overrightarrow{PN}+\frac{1}{2}\overrightarrow{NM}=0,\overrightarrow{PM}\bullet \overrightarrow{PF}=0$.

(1) Find the equation of the trajectory $E$ of the moving point $N$;

(2) A line $l$ passing through point $F$ intersects curve $E$ at two points $A$ and $B$. Find the minimum value of the area of $\Delta OAB$.

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