
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 the sequence $\{a_n\}$ with $a_1 = \frac{7}{6}$, and for any positive integer $n$, the quadratic equation in $x$, given by $a_n x^2 - a_{n+1} x + 1 = 0$, has roots $\alpha_n$ and $\beta_n$ that satisfy the condition $6 \alpha_n - 2 \alpha_n \beta_n + 6 \beta_n = 3$. Find the general formula for $\{a_n\}$.

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