
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
$(1)$ Find the minimum value of $y=\frac{{x}^{2}+7x+10}{x+1}$ where $x \gt -1$. <br/>$(2)$ Given $x \gt 0$, $y \gt 0$, and $2x+8y-xy=0$, if the inequality $a\leqslant x+y$ always holds, find the range of real number $a$.

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