
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 test, \( 3n \) students participate, who are located in three rows of \( n \) students in each. The students leave the test room one by one. If \( N_{1}(t), N_{2}(t), N_{3}(t) \) denote the numbers of students in the first, second, and third row respectively at time \( t \), find the probability that for each \( t \) during the test,
$$
|N_{i}(t) - N_{j}(t)| < 2, \quad i \neq j, \quad i, j = 1, 2, \ldots.
$$

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