
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
Let $\{a_n\}$ be a geometric sequence with first term $a_1=1$ and sum of the first $n$ terms $S_n$. The sequence satisfies the recurrence relation $S_{n+2}=4S_n+3$. Determine the common ratio of $\{a_n\}$.

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