
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 the length error $X$ (unit: mm) of a batch of parts follows a normal distribution $N\left( \mu ,\sigma^{2} \right)$, and its density function reaches the maximum value $\frac{1}{3\sqrt{2\pi }}$ when $X=0$, calculate the probability that its length error falls within the interval $(3,6)$.

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