
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 the function $f(x)=a^{x-1}-2$ $(a > 0, a \neq 1)$, determine the minimum value of $\frac{1}{m}+ \frac{2}{n}$ if the graph of the function always passes through a fixed point that lies on the line $mx-ny-1=0$, where $m > 0, n > 0$.

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