
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 $y=a^{x-1}+1$ $(a > 0$ and $a \neq 1)$ passes through a fixed point $P$, and point $P$ lies on the line $2mx+ny-4=0$ $(mn > 0)$, find the minimum value of $\frac{4}{m} + \frac{2}{n}$.

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