
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, X, Y, and Z, each of which is worth a whole number of dollars from $1 to $9999 inclusive. The contestant wins the prizes by correctly guessing the price of each prize in the order X, Y, Z. As a hint, the digits of the three prices are given. On a particular day, the digits given were $2, 2, 2, 3, 3, 3, 3$. Find the total number of possible guesses for all three prizes consistent with the hint, given the condition that prices of X and Z must contain the same number of digits.

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