
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
In the arithmetic sequence $\left\{ {{a}_{n}} \right\}$, it is known that $({{a}_{2}}+{{a}_{6}}+{{a}_{10}}=15)$ and $({{a}_{4}}+{{a}_{5}}+{{a}_{6}}+...+{{a}_{12}}=99)$. Find the general term formula $({{a}_{n}})$ and the sum of the first $20$ terms $({{S}_{20}})$.

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