
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
Alice and Bob each draw one number from 50 slips of paper numbered from $1$ to $50$ placed in a hat. Alice says, "I can't tell who has the larger number." Bob then says, "I am certain who has the larger number." Understanding Bob's certainty, Alice asks Bob if his number is prime. Bob answers, "Yes." Alice then says, "In that case, when I multiply your number by $100$ and add my number, the result is a perfect square. What could my number possibly be?"
**A)** $24$  
**B)** $61$  
**C)** $56$  
**D)** $89$

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