
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 the function $f(x)=\frac{2x}{3x+2}$, the sequence ${a_n}$ satisfies $a_1=1$ and $a_{n+1}=f(a_n)$.

1. Find the general formula for the sequence ${a_n}$;
2. (Logic) Let $b_n = a_n a_{n+1}$, and the sum of the first $n$ terms of the sequence ${b_n}$ is $S_n$. If $S_n < \frac{m-2016}{2}$ holds for all positive integers $n$, find the minimum positive integer value of $m$.
3. (Text) Let $b_n = \frac{1}{a_n}\times 2^n$, and the sum of the first $n$ terms of the sequence ${b_n}$ is $S_n$. Find $S_n$.

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