
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
The sum of the first $n$ terms of the sequence $\{a_n\}$ is denoted by $S_n$, $a_1 = t$, and the point $(S_n, a_{n+1})$ lies on the line $y = 3x + 1$ for $n \in N^*$.  
(Ⅰ) For what value of the real number $t$ is the sequence $\{a_n\}$ a geometric sequence?  
(Ⅱ) Under the conclusion of (Ⅰ), let $b_n = \log_{4}a_{n+1}$ and $c_n = a_n + b_n$, and let $T_n$ be the sum of the first $n$ terms of the sequence $\{c_n\}$. Find $T_n$.

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