
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 offers a contestant three prizes D, E, and F, each worth a whole number of dollars from $1 to $9999 inclusive. To win, the contestant must correctly guess the price of each prize in the order D, E, F. As a hint, the digits of the three prices given on a certain day were $1, 2, 2, 3, 3, 3, 4$. Find the total number of possible guesses for all three prizes consistent with the hint.

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