
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 evaluate: $\left(\frac{a+1}{2a-2}-\frac{5}{2{a}^{2}-2}-\frac{a+3}{2a+2}\right)÷\frac{{a}^{2}}{{a}^{2}-1}$, where the value of $a$ is chosen as an appropriate integer from the solution set of the inequality system $\left\{\begin{array}{l}{a-\sqrt{5}＜0}\\{\frac{a-1}{2}＜a}\end{array}\right.$.

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