
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
Let the sequence $\{a_n\}$ have a sum of the first $n$ terms denoted by $S_n$, and it satisfies $a_n=2-S_n$ $(n\in\mathbb{N}^*)$.  
(I) Find the values of $a_1$, $a_2$, $a_3$, $a_4$ and write down the general formula;  
(II) Use a three-step proof to demonstrate that the sequence $\{a_n\}$ is a geometric sequence.

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