
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
Using the information provided in the table below:

$$2^8 = 256, \quad 2^9 = 512, \quad 10^2 = 100, \quad 10^3 = 1000,$$

what can be determined about the smallest interval in which $\log_{10}{2}$ falls?
A) $\frac{1}{4} \text{ and } \frac{1}{3}$
B) $\frac{1}{5} \text{ and } \frac{1}{2}$
C) $\frac{2}{9} \text{ and } \frac{3}{8}$
D) $\frac{2}{8} \text{ and } \frac{4}{9}$

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