
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
There is a cage with 10 cats, including 7 white cats and 3 black cats. The cage door is opened slightly, allowing only one cat to exit at a time. The cats rush out one by one. If all 10 cats exit the cage, let \( X \) represent the number of segments into which the 7 white cats are divided by the 3 black cats. For example, in a certain exit sequence, \( X \) can be 3 because the 7 white cats are divided into 3 segments. Find the distribution of \( X \).

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