
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
Simplify the following expression:

$$
\frac{(x-1) \sqrt{x^{2}-6 x+8}}{(x-2) \sqrt{x^{2}-4 x+3}}+\frac{(x-5) \sqrt{x^{2}-4 x+3}}{(x-3) \sqrt{x^{2}-7 x+10}}
$$

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