
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 diameters of balls for bearings are controlled as follows: if the ball does not pass through a hole with diameter $d_{1}$ but passes through a hole with diameter $d_{2} > d_{1}$, its size is considered acceptable. If any of these conditions are not met, the ball is rejected. It is known that the diameter of the ball is a random variable $X$ distributed according to a normal law, with the mathematical expectation of this quantity $a = \left(d_{1} + d_{2}\right) / 2$ and the standard deviation $\sigma = \left(d_{2} - d_{1}\right) / 4$. Find the probability that the tested ball will be rejected.

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