
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 $B$ respectively, which intersect at point $P$.
(I) Find the coordinates of point $P$;
(II) Let $M$ be any point on the parabolic segment between $A$ and $B$. Assume that $\overrightarrow{PM} = \lambda \overrightarrow{PA} + \mu \overrightarrow{PB}$, determine whether $\sqrt{\lambda} + \sqrt{\mu}$ is a constant value. If it is, find this constant value; if not, explain the reason.

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