
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-geometric sequence $\{a\_n\}$, it is known that $a\_1+a\_3=5$ and $a\_2+a\_4=10$.

1. Find the general term formula $a\_n$ of the sequence.
2. Find the sum $s\_n$ of the first $n$ terms of the sequence.

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