
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
1. Line $l$ intersects the parabola $y^2=8x$ at points $A$ and $B$, and passes through the focus $F$ of the parabola. Given that $A(8,8)$, find the distance from the midpoint of segment $AB$ to the directrix.
2. Given points $A(4,1,3)$, $B(2,3,1)$, $C(3,7,-5)$, and a point $P(x,-1,3)$ which lies on the plane determined by $ABC$, find the value of $x$.

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