
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
Consider a modified lottery where a participant picks five different integers from 1 through 30. Tom chooses his numbers so that both the sum of their base-two logarithms is an integer, and the chosen numbers form an arithmetic progression. What is the probability that Tom's ticket will have the same numbers, considering the same constraints, as the winning ticket?
A) 1/5
B) 1/4
C) 1/3
D) 1/2
E) 1

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