
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
Create a five-digit number $\overline{a_1a_2a_3a_4a_5}$ using the digits 1, 2, 3, and 4. When randomly choosing one of these numbers, find the probability that for any positive integer $j$ ($1 \leq j \leq 5$), there exists at least one other positive integer $k$ ($1 \leq k \leq 5$ and $k \neq j$) such that $a_j = a_k$.

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