
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
Given the data $10^4 = 10,000$, $10^5 = 100,000$, $2^{12} = 4096$, and $2^{15} = 32,768$, determine the most accurate range for $\log_{10}{2}$.
A) $\log_{10}(2) < \frac{1}{3}$
B) $\log_{10}(2) > 0.30$
C) $\log_{10}(2) \approx 0.3010$
D) $\log_{10}(2) > \frac{4}{13}$

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