
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 sequence $\{a_n\}$, $a_1=2$, $a_{n+1}=a_n+c\cdot2^n$ (where $c$ is a constant, $n=1,2,3,\ldots$), and $a_1, a_2, a_3$ form a geometric sequence with a common ratio not equal to 1.  
(Ⅰ) Find the value of $c$.  
(Ⅱ) Find the general formula for $\{a_n\}$.

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