
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 $\{a_n\}$, $a_1=1$, $a_{n+1} = \frac{2a_n}{2+a_n}$ ($n \in \mathbb{N}^+$), try to write out the first 4 terms of this sequence, guess the general formula of this sequence, and provide a proof.

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