
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 natural number has digits $a$, $b$, and $c$ in the hundreds, tens, and units places, respectively. Given that $a, b, c \in \{1,2,3,4\}$ and $a, b, c$ are all different, determine the probability that this number is a "convex number".

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