
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 five-digit number without repeated digits $a_1a_2a_3a_4a_5$, when $a_1 < a_2$, $a_2 > a_3$, $a_3 < a_4$, $a_4 > a_5$ is called a wave number. What is the probability that a five-digit number formed by the digits $1$, $2$, $3$, $4$, $5$ without any repetition is a wave number?

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