
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
When $a > 0$, $a \neq 1$, the graph of the function $f(x)=\log_{a}(x-1)+1$ always passes through a fixed point $A$. If point $A$ lies on the line $mx-y+n=0$, then the minimum value of $4^{m}+2^{n}$ is ______.

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