
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 that a random variable following the normal distribution $N(\mu, \sigma^2)$ takes values in the intervals $(\mu-\sigma, \mu+\sigma)$, $(\mu-2\sigma, \mu+2\sigma)$, and $(\mu-3\sigma, \mu+3\sigma)$ with probabilities of $68.26\%$, $95.44\%$, and $99.74\%$, respectively. The density function of a certain normal curve is an even function, and the maximum value of this function is $\frac{1}{2\sqrt{2\pi}}$. The probability that the population falls within the interval $[-4,-2]$ is _______.

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