
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 the conditions for automobile license plates in Mathland, where the first symbol must be a vowel (A, E, I, O, or U), the second and third symbols must be two different letters among the 21 non-vowels, and the fourth symbol must be a digit (0 through 9), calculate the probability that the plate will read "AMC8".

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