
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 a geometric sequence $\{a_n\}$ where the first term is $a_1=2$ and the common ratio is $q$ (with $q$ being a positive integer), it satisfies that $3a_3$ is the arithmetic mean of $8a_1$ and $a_5$. The sequence $\{a_n\}$ also satisfies the equation $2n^2 - (t + b_n)n + \frac{3}{2}b_n = 0$ ($t$ ∈ R, $n$ ∈ N*).  
(1) Find the general term formula of the sequence $\{a_n\}$.  
(2) Determine the value of the real number $t$ so that the sequence $\{b_n\}$ is an arithmetic sequence.

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