
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 first, then find the value;  
$(1)$ When $a=\sqrt{3}-1$, find the value of $(a^2+a)⋅\frac{a+1}{a}$;  
$(2)$ When $a=\frac{1}{2}$, find the value of $\frac{a+1}{a^2-1}-\frac{a+1}{1-a}$.

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