
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
Professor Vector selects seven different integers from $1$ through $60$, inclusive. He chooses his numbers so that the sum of the base-ten logarithms of his seven numbers is an integer. This implies that the integers on the winning lottery ticket have the same property—the sum of the base-ten logarithms is an integer. What is the probability that Professor Vector holds the winning ticket?
**A)** $\frac{1}{386206920}$
**B)** $\frac{1}{100000000}$
**C)** $\frac{1}{123456789}$
**D)** $\frac{1}{7}$

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