
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
Given 3 identical black balls and 3 identical white balls lined up from left to right, the arrangement is considered "valid" if, starting from any position (including that position) to the right, the number of black balls is not less than the number of white balls. What is the probability of a "valid" arrangement?

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