
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 $f(x)=2\sin ( \frac {π}{3}x+ \frac {π}{6})$ and the set $M={x||f(x)|=2,x > 0}$, arrange the elements in $M$ from smallest to largest to form a sequence ${a_{n}}(n∈N^{*})$.
(1) Find the general term formula of the sequence ${a_{n}}$;
(2) Let the sequence ${b_{n}}$ satisfy: $b_{1}=1,b_{n+1}=b_{n}+a_{2^{n}}$, find the general term formula of the sequence ${b_{n}}$.

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