
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
A club decides to issue special IDs consisting of five characters using the four letters in AIME and the five digits in 2023. Each ID must adhere to restrictions where no character appears more times than it appears in "AIME" or "2023". How many unique IDs can the club issue if "2" can appear up to two times and "3" can also appear up to two times? Determine $\frac{N}{10}$, where $N$ is the total number of unique IDs.

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