
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 only the values $10^3 = 1000$, $10^4 = 10,000$, $2^{10} = 1024$, and $2^{12} = 4096$, what can be determined as the tightest bounds for $\log_{10}(2)$?
A) $\frac{1}{5} \; \text{and} \; \frac{4}{10}$
B) $\frac{1}{4} \; \text{and} \; \frac{4}{11}$
C) $\frac{1}{4} \; \text{and} \; \frac{4}{10}$
D) $\frac{1}{3} \; \text{and} \; \frac{4}{11}$
E) $\frac{3}{10} \; \text{and} \; \frac{40}{132}$

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