
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 find the value of: $\frac{{a-1}}{{{a^2}-2a+1}}\div (\frac{{{a^2}+a}}{{{a^2}-1}}+\frac{1}{{a-1}}$), where $a=\sqrt{3}-1$.

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