
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 ${a_{n}}$ with the sum of its first $n$ terms denoted as $S_{n}$, it satisfies the condition $S_{n+3}=8S_{n}+3$ for any positive integer $n$. Find $a_{1}=$ _______ and the common ratio $q=$ _______.

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