
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 3 identical black balls and 3 identical white balls in a row from left to right. If any position (including that position) to the left always has at least as many black balls as white balls, we call this arrangement a "valid arrangement". What is the probability of having a "valid arrangement"?

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