
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
The graph of the function $f(x) = a^{x-1} + 3$ ($a > 0$, and $a\neq 1$) passes through a fixed point $P$, and point $P$ lies on the line $mx + ny - 1 = 0$ ($m > 0$ and $n > 0$). The minimum value of $\frac{1}{m} + \frac{4}{n}$ is _____.

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