
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. Let $l_1$ and $l_2$ be tangent lines to the parabola at points $A$ and $B$ respectively, which intersect at point $P$.

1. Find the coordinates of point $P$.
2. Let $M$ be any 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 value; otherwise, explain the reason.

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