
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
Teacher Lin wants to choose 2 different letters from $\{A,B,C\}$ and 3 different numbers from $\{1,3,5,7\}$ to form the last five digits of a license plate number in the form of $J\times \times \times \times \times$, with the condition that the numbers chosen must not be adjacent to each other. Calculate the number of valid license plate numbers.

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