
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 arithmetic sequence $\{{a_n}\}$ with ${a_1}=1$ and the sum of the first $n$ terms ${S_n}$, if $\frac{{S_{19}}}{19}-\frac{{S_{17}}}{17}=6$, calculate the value of ${S_{10}}$.

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