
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 $x\_1$, $x\_2$, $x\_3$, $x\_4$ be a permutation of the natural numbers $1$, $2$, $3$, $4$, and satisfy $|x\_1-1|+|x\_2-2|+|x\_3-3|+|x\_4-4|=6$. Determine the number of such permutations.

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