
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 follows a normal distribution $N(\mu, \sigma^2)$, the probabilities of the variable falling within the intervals $(\mu - \sigma, \mu + \sigma)$, $(\mu - 2\sigma, \mu + 2\sigma)$, and $(\mu - 3\sigma, \mu + 3\sigma)$ are 68.26%, 95.44%, and 99.74% respectively. A particular normal distribution curve has an even density function and its maximum value is $\frac{1}{2 \sqrt{2\pi}}$. Find the probability that the distribution falls within the interval \[-4, -2\].

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