
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 $\{b_n\}$ whose sum of the first $n$ terms is $S_n$, and $b_1=1$, $b_{n+1}= \frac {1}{3}S_n$.  
$(1)$ Find the values of $b_2$, $b_3$, $b_4$;  
$(2)$ Find the general formula for $\{b_n\}$;  
$(3)$ Find the value of $b_2+b_4+b_6+\ldots+b_{2n}$.

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