
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
There are 10 cards, each with two different numbers from the set {1, 2, 3, 4, 5}, and no two cards have the exact same pair of numbers. These 10 cards are placed in five boxes labeled 1, 2, 3, 4, and 5. A card labeled with numbers i and j can only be placed in box i or box j. A placement is called "good" if and only if the number of cards in box 1 is greater than the number of cards in each of the other boxes. Find the total number of good placements.

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