
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
On a table, there are 10 cards numbered $1, 1, 2, 2, 3, 3, 4, 4, 5, 5$. These 10 cards are shuffled and arranged in a row from left to right. Then, the number of cards between the two 1s, the two 2s, the two 3s, the two 4s, and the two 5s are counted. What is the maximum sum of these 5 numbers?

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