
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:
$$( \frac {x}{x-1}- \frac {x}{x^{2}-1})÷ \frac {x^{2}-x}{x^{2}-2x+1}$$
where $$x= \sqrt {2}-1$$

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