
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
Given the number $y$ represented as \[ y = \frac{b_1}{2} + \frac{b_2}{2^3} + \cdots + \frac{b_{15}}{2^{29}} \], where $b_1, b_2, ..., b_{15}$ are each either 0 or 3, determine the range of possible values for $y$.

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