
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 large province of Mathalia, all automobile license plates have five symbols. The first two must be different vowels (A, E, I, O, or U), the next two must be different non-vowels, and the last must be a digit (0 through 9). Calculate the probability that the plate will read "AEMC9".

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