
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 presents a contestant with three prizes X, Y, and Z. Each prize's value is a whole number of dollars ranging from $1 to $9999. To win, the contestant must correctly guess the prices of the prizes in order. One day, the hint provided includes the digits $1, 1, 2, 2, 3, 3, 3$. Determine the total number of valid guesses for the prices of prizes X, Y, and Z consistent with the provided hint.

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