
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
Arrange four identical red balls and four identical black balls in a row, and then number them from left to right as 1, 2, …, 8. How many arrangements are there such that the sum of the numbers on the red balls is less than the sum of the numbers on the black balls?

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