
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
Using the digits $1$, $2$, $3$, $4$,

$(1)$ How many three-digit numbers can be formed?

$(2)$ How many three-digit numbers without repeating digits can be formed?

$(3)$ How many three-digit numbers without repeating digits can be formed, where the digit in the hundreds place is greater than the digit in the tens place, and the digit in the tens place is greater than the digit in the units place?

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