
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 the arithmetic sequence $\{a_n\}$, $a_2 = 5$, $a_1 + a_3 + a_4 = 19$.
(Ⅰ) Find the general term formula for the sequence $\{a_n\}$;
(Ⅱ) Suppose for the sequence $\{b_n\}$, the sum of the first n terms is $S_n$, and $S_n + \frac{a_n - 1}{2^n} = \lambda$ (where $\lambda$ is a constant). Let $c_n = b_{n+1}$ (for $n \in \mathbb{N}^*$). Find the sum of the first n terms $T_n$ for the sequence $\{c_n\}$.

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