
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
An urn contains \(n\) white balls and \(m\) black balls, next to the urn is a box with a sufficiently large number of black balls. The following operation is performed: a pair of balls is drawn randomly from the urn; if they are of the same color, a black ball from the box is placed into the urn; if they are of different colors, the white ball is returned to the urn. The operation is repeated until there is only one ball left in the urn. What is the probability that the last remaining ball will be white?

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