
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 $f(x)=\log_{a}(x-1)+1$ $(a > 0$ and $a \neq 1)$ always passes through a fixed point $M$, and point $M$ lies on the line $\frac{x}{m}+ \frac{y}{n}=1$ $(m > 0,n > 0)$, find the minimum value of $m+n$.

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