
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
In triangle $\triangle ABC$, the lengths of the sides opposite to angles A, B, and C are a, b, and c respectively. a and c are the first term $a_1$ and the second term $a_2$ of the geometric sequence $\{a_n\}$, respectively. The solution set to the inequality $-x^2+6x-8>0$ is $\{x|a<x<c\}$. Find the general term formula for the sequence $\{a_n\}$.

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