
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 that $m$ and $n$ are positive real numbers satisfying $m + n = 1$, find the value of $\alpha$ such that when the minimum value of $\frac{1}{m} + \frac{16}{n}$ is attained, the curve $y = x^\alpha$ passes through the point $P\left( \frac{m}{5}, \frac{n}{4} \right)$.

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