
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
For positive integers \( n \), let \( D(n) \) denote the number of pairs of different adjacent digits in the binary (base two) representation of \( n \). Additionally, let \( S(n) \) be the sum of the digits in the binary representation of \( n \). For example, for \( n = 21 \), \( D(21) = 4 \) and \( S(21) = 3 \). Determine how many positive integers less than or equal to 100 are there for which \( D(n) = 2 \) and \( S(n) = 3 \).
- **A)** 5
- **B)** 7
- **C)** 8
- **D)** 9
- **E)** 10

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