
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 a line $l$ passing through the focus $F(1,0)$ of the parabola $y^2=2px$ ($p>0$) intersecting the parabola at points $M$ and $N$,
(Ⅰ) Write the standard equation of the parabola and the equation of its directrix;
(Ⅱ) $O$ is the origin of coordinates, and the lines $MO$ and $NO$ intersect the directrix at points $P$ and $Q$, respectively, find the minimum value of $|PQ|$.

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