
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 with a common ratio of $q (q > 0)$, let $S_n$ denote the sum of its first $n$ terms. If $S_2 = 3a_2 + 2$ and $S_4 = 3a_4 + 2$, find the value of $a_1$.

A) $-2$
B) $-1$
C) $\frac{1}{2}$
D) $\frac{2}{3}$

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