
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
With the use of the tabular information $10^3=1000$, $10^4=10,000$, $2^{11}=2048$, $2^{12}=4096$, $2^{13}=8192$, $2^{14}=16384$, determine the narrowest range for $\log_{10}(\sqrt{2})$.
**A)** $\frac{3}{22} \; \text{and} \; \frac{1}{14}$
**B)** $\frac{3}{22} \; \text{and} \; \frac{1}{7}$
**C)** $\frac{3}{11} \; \text{and} \; \frac{1}{7}$
**D)** $\frac{3}{14} \; \text{and} \; \frac{1}{6}$
**E)** $\frac{3}{21} \; \text{and} \; \frac{1}{14}$

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