
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 the doors on public buses is designed so that the probability of a man hitting his head is no greater than 0.0228. Assuming that the height of men, $X$, follows a normal distribution $N(170, 7^2)$ (in centimeters), and considering the following probabilities:
$$ P(\mu-\sigma < X \leq \mu+\sigma) = 0.6826, $$
$$ P(\mu-2\sigma < X \leq \mu+2\sigma) = 0.9544, $$
$$ P(\mu-3\sigma < X \leq \mu+3\sigma) = 0.9974, $$
the height of the bus doors (in centimeters) should be designed to be at least __________ cm.

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