
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
In a box, there are $12$ table tennis balls, among which $9$ are new and $3$ are old. If $3$ balls are randomly taken out of the box for use and then put back into the box, determine the value of $P(X=4)$.

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