
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 an arithmetic sequence ${{a_{n}}}$, the sum of its first $n$ terms is denoted as ${{S_{n}}}$. The third term of the sequence, $a_{3}$, is equal to 3, and the tenth term, $a_{10}$, is equal to 384. Find the common ratio, $q$, and the general formula for the sum of the first $n$ terms, ${S_{n}}$.

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