
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 three identical black balls and three identical white balls in a row from left to right. If the number of black balls is always greater than or equal to the number of white balls counting from any position (inclusive) to the left, then such an arrangement is called a "valid arrangement". What is the probability of getting a "valid arrangement"?

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