
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
Consider the algebraic fraction:
$$\frac{x^2 - 4x + 3}{x^2 - 3x + 2} \div \frac{x^2 - 6x + 9}{x^2 - 7x + 10}$$
Simplify the given expression.
A) \(\frac{x-5}{x-3}\)  
B) \(\frac{x-3}{x-5}\)  
C) \(\frac{x+1}{x-1}\)  
D) \(1\)  
E) \(2\)

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