
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
In the redesigned country of Hexland, all automobile license plates must adhere to a new format with four symbols. The first must be a vowel (A, E, I, O, U, Y), the second and third must be two different letters among the 22 non-vowels (including all alphabets except A, E, I, O, U, Y), and the fourth must be a hexadecimal digit (0 through 9, A through F). Determine the probability that a randomly selected license plate reads "EYB5".
A) $\frac{1}{44,352}$
B) $\frac{1}{22,176}$
C) $\frac{1}{10,588}$
D) $\frac{1}{5,544}$
E) $\frac{1}{2,772}$

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