
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
Find the probability that a five-digit number with no repeated digits, $a_1a_2a_3a_4a_5$, is a "wavelike number" where $a_1 < a_2$, $a_2 > a_3$, $a_3 < a_4$, and $a_4 > a_5$. For example, 89674 is a wavelike number. Calculate the probability that a wavelike number can be formed using the digits 1, 2, 3, 4, and 5 without repetition.

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