
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
Random variable $X$ follows a normal distribution $X\sim N(10$,$\sigma ^{2})$. If $P\left(X \gt 12\right)=m$ and $P\left(8\leqslant X\leqslant 10\right)=n$, then the minimum value of $\frac{2}{m}+\frac{1}{n}$ is ______.

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