
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 $\{a_n\}$, $a_1=1$, $a_{n+1}= \frac{2a_n}{2+a_n} (n\in\mathbb{N}^*)$.

(Ⅰ) Calculate $a_2$, $a_3$, $a_4$;

(Ⅱ) Conjecture the general formula of this sequence and provide a proof.

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