
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 are three boxes \(A\), \(B\), and \(C\) containing 100, 50, and 80 balls respectively. Each box has a certain number of black balls. It is known that box \(A\) contains 15 black balls. If a box is chosen randomly and then a ball is randomly drawn from that box, the probability of drawing a black ball is \(\frac{101}{600}\). Determine the maximum number of black balls that can be in box \(C\).

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