
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
How many different positive three-digit integers can be formed using only the digits in the set $\{1, 3, 3, 4, 4, 4, 7\}$ if no digit may be used more times than it appears in the set of available digits?

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