
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
Let $abcd$ be a four-digit number, where $a$, $b$, $c$, and $d$ are Arabic numerals, and $a\leqslant b\leqslant c\leqslant d$. Find the maximum value of the expression $|a-b|+|b-c|+|c-d|+|d-a}$.

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