
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 positive geometric sequence $\{a_n\}$, $a_1=2$, and $a_2$, $a_1+a_2$, $a_3$ form an arithmetic sequence.
(Ⅰ) Find the general formula for the sequence $\{a_n\}$;
(Ⅱ) Let $$b_{n}=(1- \frac {2}{a_{n}})^{2}+a(1+ \frac {1}{a_{n}})$$ ($n\in\mathbb{N}^*$), if $a\in[0,2]$, find the minimum term of the sequence $\{b_n\}$.

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