
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 bag, there are $n$ ($n \in \mathbb{N}^*$) white balls and 3 red balls. Balls are drawn one at a time from the bag. If a red ball is drawn, it is not replaced, and the drawing continues; if a white ball is drawn, the drawing stops. Let $X$ be the number of times balls are drawn. If $P(X=2) = \frac{7}{30}$, then the value of $n$ is \_\_\_\_\_\_.

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