
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
For values of \( x \) between $0$ and $5$, evaluate the maximum and minimum values of the expression
$$\frac{x^2 - 4x + 5}{2x - 4}.$$
A) Minimum value of -1 and maximum value of 1  
B) Minimum value of 1 and maximum value of -1  
C) Maximum value only of 0  
D) No extremum values within the domain

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