
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 all numbers $y$ of the form
\[y = \frac{b_1}{5} + \frac{b_2}{5^2} + \cdots + \frac{b_{15}}{5^{15}}\]
where each $b_i$ (for $i=1,2,...,15$) can either be $0$ or $3$.
A) $0 \leq y < 0.45$
B) $0 \leq y < 0.9$
C) $0.45 \leq y < 0.9$
D) $0 \leq y < 0.55$
E) $0.6 \leq y < 0.9$

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