
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
Can the reader name the sum of all integers composed of the four digits $1, 2, 3, 4$? In other words, we need to calculate the sum of numbers like $1234, 1423, 4312$, etc. Understandably, one could list all such numbers in sequence and then sum them. However, it is more interesting to find a simple rule that can be used to find the sums of numbers composed of four different randomly chosen (non-zero) digits.

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