
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
Let $T$ be the set of integers between $1$ and $2^{50}$ whose binary expansions have exactly three $1$'s. If a number is chosen at random from $T,$ the probability that it is divisible by $7$ is $p/q,$ 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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