
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
Determine the range of values for the number \(y\) expressed as:
\[ y = \frac{b_1}{4} + \frac{b_2}{4^2} + \cdots + \frac{b_{30}}{4^{30}} \]
where \(b_1, b_2, \ldots, b_{30}\) each can be either 1 or 3.
A) \(0 \leq y < \frac{1}{4}\)  
B) \(\frac{1}{3} \leq y < 1\)  
C) \(\frac{5}{6} \leq y < 1\)  
D) \(0 \leq y < \frac{1}{3}\)  
E) \(\frac{1}{2} \leq y \leq 1\)

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