
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 random variable $X$ follows a normal distribution $X \sim N(10, \sigma^2)$, with probability $m$ that $X > 12$ and probability $n$ that $8 \leqslant X \leqslant 10$, find the minimum value of $\frac{2}{m} + \frac{1}{n}$.

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