
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: $(a-1-\frac{3}{{a+1}})÷\frac{{{a^2}-4a+4}}{{a+1}}$, where the value of $a$ is selected as an integer from the solution set of the inequality $-\sqrt{2}＜a＜\sqrt{5}$.

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