
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
Dr. Loxley participates in a game where she has to choose six different integers from $1$ to $49$, inclusive. She selects her numbers such that the product of these numbers results in a perfect square. The integers on the winning ticket also form a product that is a perfect square. What is the probability that Dr. Loxley holds the winning ticket?
A) 1/25
B) 1/50
C) 1/100
D) 1/200

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