
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
The famous mathematician Hua Luogeng once said: "Combining numbers and shapes is always good, dividing things apart leads to endless repairs." In fact, many algebraic problems can be transformed into geometric problems for resolution. For example, $\sqrt{(x-a)^{2}+(y-b)^{2}}$ can be transformed into the distance between point $M\left(x,y\right)$ and point $N\left(a,b\right)$ on a plane. Based on the above viewpoint, the maximum value of $\sqrt{{x}^{2}-2x+5}-\sqrt{{x}^{2}+1}$ is ______.

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