
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 is a box containing  $100$  balls, each of which is either orange or black. The box is equally likely to contain any number of black balls between  $0$  and  $100$ , inclusive. A random black ball rolls out of the box. The probability that the next ball to roll out of the box is also black can be written in the form  $\tfrac{p}{q}$  where  $p$  and  $q$  are relatively prime positive integers. Find  $p + q$ .

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