
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 a random variable that follows a normal distribution $N(\mu, \sigma^2)$, the probability of its value falling within the intervals $(\mu-\sigma, \mu+\sigma)$, $(\mu-2\sigma, \mu+2\sigma)$, and $(\mu-3\sigma, \mu+3\sigma)$ are $68.27\%$, $95.45\%$, and $99.73\%$, respectively. A high school is ordering school uniforms for $10000$ students. Assume that the students' heights (in cm) follow a normal distribution $N(173, 25)$. Approximately how many uniforms should be prepared for students with heights in the range of $158 \sim 188$ cm?

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