
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 $\{a_n\}$ be an arithmetic sequence, and $\{b_n\}$ be a geometric sequence. Let $T_n$ be the sum of the first $n$ terms of $\{b_n\}$, with $a_1=b_1=1$, and it satisfies $$\sqrt {a_{2}+2}+ \sqrt {b_{2}-2}=2 \sqrt {2}$$, when $a_{2}+b_{2}$ takes the minimum value,  
(1) Find $T_n$;  
(2) Let $S_n$ be the sum of the first $n$ terms of $\{|a_n|\}$, find $S_n$.

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