
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
A certain city is assessing the physical fitness of high school students. It is stipulated that a physical fitness index value not less than $60$ is considered qualified. Now, $100$ high school students are randomly selected from the city, and their physical fitness index values are denoted as $x_{i}(i=1,2,3,\ldots ,100)$. After calculation, it is found that $\sum_{i=1}^{100}x_{i}=7200$ and $\sum_{i=1}^{100}{x}_{i}^{2}=100\times (72^{2}+36)$. If the physical fitness index values of high school students in the city follow a normal distribution $N(\mu $,$\sigma ^{2})$, estimate the percentage of high school students in the city with qualified physical fitness. (Round your answer to $0.1\%$)<br/>Reference data: If a random variable $X$ follows a normal distribution $N(\mu $,$\sigma ^{2})$, then $P\left(\mu -\sigma \leqslant X\leqslant \mu +\sigma \right)\approx 0.6827$, $P\left(\mu -2\sigma \leqslant X\leqslant \mu +2\sigma \right)\approx 0.9545$, $P\left(\mu -3\sigma \leqslant X\leqslant \mu +3\sigma \right)\approx 0.9973$.

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