
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
If $F$ is the focus of the parabola $C: y^{2}=2px\left(p > 0\right)$, $P$ is any point on the parabola $C$, the minimum value of $PF$ is $1$, and $A$ and $B$ are two points on the parabola $C$ such that $|AF|+|BF|=6$, determine the distance from the midpoint of segment $AB$ to the $y$-axis.

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