
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
The sum of the first n terms of the sequence $\{a_n\}$ is $S_n$. If the terms of the sequence $\{a_n\}$ are arranged according to the following rule: $$\frac {1}{2}, \frac {1}{3}, \frac {2}{3}, \frac {1}{4}, \frac {2}{4}, \frac {3}{4}, \frac {1}{5}, \frac {2}{5}, \frac {3}{5}, \frac {4}{5}, \ldots, \frac {1}{n}, \frac {2}{n}, \ldots, \frac {n-1}{n}, \ldots$$ If there exists a positive integer k such that $S_{k-1} < 10$ and $S_k > 10$, then $a_k = \_\_\_\_\_\_$.

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