
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
Identical red balls and three identical black balls are arranged in a row, numbered from left to right as 1, 2, 3, 4, 5, 6. Calculate the number of arrangements where the sum of the numbers of the red balls is less than the sum of the numbers of the black balls.

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