
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
Let $A$ and $B$ be two distinct points on the parabola $y^{2}=x$, with their vertical coordinates being $-1$ and $2$, respectively. Draw tangent lines $l_{1}$ and $l_{2}$ to the parabola at points $A$ and $B$, which intersect at point $P$.
(I) Determine the coordinates of point $P$.
(II) Let $M$ be an arbitrary point on the parabolic segment between $A$ and $B$. Assume $\overrightarrow{PM}=λ \overrightarrow{PA}+μ \overrightarrow{PB}$, determine whether $\sqrt {λ}+ \sqrt {μ}$ is a constant value. If it is, find this constant value; otherwise, explain the reason.

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