
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 with digits in the hundreds, tens, and units places denoted as $a$, $b$, $c$ is called a "concave number" if and only if $a > b$, $b < c$, such as $213$. If $a$, $b$, $c \in \{1,2,3,4\}$, and $a$, $b$, $c$ are all different, then the probability of this three-digit number being a "concave number" is ____.

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