
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
Evaluate the expression $\frac{x^2 - 4x + 3}{x^2 - 7x + 12} \div \frac{x^2 - 4x + 4}{x^2 - 6x + 9}$ when simplified.
**A)** $\frac{(x-1)}{(x-4)}$
**B)** $\frac{(x-1)(x-3)}{(x-4)(x-2)}$
**C)** $\frac{(x-1)(x-3)^2}{(x-4)(x-2)^2}$
**D)** $1$
**E)** $\frac{(x-3)}{(x-2)}$

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