
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 $m + n = 1$ and that the expression $\frac{1}{m} + \frac{9}{n}$ takes the minimum value, and if the function $y = x^{\alpha}$ passes through the point $P(m, \frac{2}{3}n)$, determine the value of $\alpha$.

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