
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
Given $x$, $y > 0$ and satisfying $x+y=1$, if the inequality $\frac{2}{x}+\frac{m}{y+1}≥9$ always holds, and the minimum value of $\frac{x}{1+y}+\frac{1+x}{x}$ is denoted as $n$, then the minimum value of $m+n$ is ______.

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