
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
Given that point $P(x_{0}, y_{0})$ is not on the line $l: Ax + By + C = 0$, then the distance from point $P$ to line $l$ is $d = \frac{{|A{x_0} + B{y_0} + C|}}{{\sqrt{{A^2} + {B^2}}}}$; by analogy, when point $P(x_{0}, y_{0})$ is on the graph of the function $y = f(x)$, the distance formula becomes $d = \frac{{|A{x_0} + Bf({{x_0}}) + C|}}{{\sqrt{{A^2} + {B^2}}}}$. According to this formula, the minimum value of $|x-2+\sqrt{1-{x^2}}|$ is ______.

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