
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
Given a sequence $\{a_n\}$ where the sum of the first $n$ terms $S_n$ satisfies $$S_{n}= \frac {1}{4}(a_{n}+1)^{2},$$ and $a_n > 0$  
(I) Find $a_1$, $a_2$;  
(II) Find the general formula for $\{a_n\}$;  
(III) Let $b_n = 20 - a_n$, ask for the maximum sum of the first several terms of the sequence $\{b_n\}$.

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