
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 $p$ white balls and $q$ black balls. Outside the box, there is a heap of black balls. Two balls are drawn from the box. If they are of different colors, the white ball is returned to the box; if they are of the same color, a black ball is put back into the box. This process is repeated until only one ball remains in the box. What is the probability that this remaining ball is white?

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