
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 $(b_1, b_2, \dots, b_6)$ be a sequence representing the first 6 non-negative powers of 2 (i.e., $2^0, 2^1, \dots, 2^5$). Construct lists such that for each $2 \leq i \leq 6$, either $2 \cdot b_i$ or $\frac{b_i}{2}$ (or both) appear somewhere before $b_i$ in the list. How many such lists are possible?
A) 16
B) 24
C) 32
D) 40
E) 48

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