
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
For each permutation $b_1, b_2, b_3, b_4, b_5$ of the integers $1, 2, 3, 4, 5$, form the sum
\[|b_1-b_2| + |b_3-b_4|\]
The average value of all such sums from all permutations can be written as $\frac{p}{q}$, where $p$ and $q$ are coprime integers. Determine $p+q$.

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