
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 game show now includes a modified hint system where the digits of the prices of three prizes A, B, and C are given as $1, 1, 1, 2, 2, 3, 3, 3, 3$. Each prize is still worth a whole number of dollars from $1$ to $9999$. Additionally, one of the prizes is guaranteed to be worth at least $1000$. Find the total number of possible arrangements for the guesses of the prices of the three prizes consistent with the hint and the additional condition.

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