
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 probability of a number starting with n in base 10 is given by $P_{10}(n) = \log_{10}\frac{n+1}{n}$, determine the value of k such that $\sum_{n=k}^{20}P_{10}(n)=\frac{\log_2 21 - \log_2 3}{1+\log_2 5}$.

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