
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 tabular information $10^3=1000$, $10^5=100,000$, $2^{15}=32,768$, and $2^{16}=65,536$, along with $\log_{10}{2}$ estimates, which among the following is the strongest statement one can make for $\log_{10}{2}$?
**A)** $\frac{1}{6} \text{ and } \frac{4}{15}$
**B)** $\frac{1}{5} \text{ and } \frac{5}{16}$
**C)** $\frac{3}{16} \text{ and } \frac{5}{15}$
**D)** $\frac{1}{15} \text{ and } \frac{5}{14}$
**E)** $\frac{1}{16} \text{ and } \frac{5}{18}$

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