
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 three-digit number has digits $x$, $y$, and $z$ in the units, tens, and hundreds place, respectively. If $y > x$ and $y > z$, then the number is called a "convex number" (e.g., 243). Given the set ${1,2,3,4}$, if three distinct numbers are selected to form a three-digit number, what is the probability that this number is a "convex number"?
A) $\frac{2}{3}$
B) $\frac{1}{3}$
C) $\frac{1}{6}$
D) $\frac{1}{12}$

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