
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 height of a bus door is designed such that the probability of a male passenger hitting his head is no more than 0.0228. Suppose the height of males, X, follows a normal distribution N(170, 7^2) (in cm). Refer to the following probabilities: P(μ − σ < X ≤ μ + σ) = 0.6826, P(μ − 2σ < X ≤ μ + 2σ) = 0.9544, P(μ − 3σ < X ≤ μ + 3σ) = 0.9974. What should be the minimum height of the bus door (in cm)?

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