
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
A box contains \(n\) white and \(m\) black balls \((n \geqslant m)\). All the balls are drawn sequentially at random. Find the probability of the following events:

(a) There will be a moment when there are equal numbers of white and black balls in the sequence of drawn balls.

(b) At any moment in the sequence of drawn balls, the number of white balls will not be less than the number of black balls.

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