
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
Given an array $(a\_1, a\_2, a\_3, a\_4, a\_5)$ consisting of a permutation of the numbers $1$, $2$, $3$, $4$, $5$, such that each permutation corresponds to only one array, and in each array, there is exactly one element $a\_i$ such that $a\_i = i$ ($i=1,2,3,4,5$). The sum of all the numbers in all distinct arrays is $\_\_\_\_\_\_$.

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