
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 and then evaluate the expression:

$$
\left( \frac{x^{2}+1}{x}+2 \right) \div \frac{(x-3)(x+1)}{x^{2}-3x}
$$

where $x+2=\sqrt{2}$.

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