
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 ${ \{ a_{n} \}}$, $a_{1}+a_{3}=8$, and $a_{4}$ is the geometric mean of $a_{2}$ and $a_{9}$. Find the first term, common difference, and the sum of the first $n$ terms of the sequence.

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