
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 randomly selected five-digit natural number formed by the digits 0, 1, 2, 3, 4 satisfies the condition $a\_1 > a\_2 > a\_3$ and $a\_3 < a\_4 < a\_5$, where $0 \leq a\_1, a\_2, a\_3, a\_4, a\_5 \leq 4$.

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