
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
A sequence ${a_n}$ satisfies $a_1=1$, $a_2=\frac {1}{2}$, and ${a_na_{n+1}}$ is a geometric sequence with a common ratio of $\frac {1}{2}$.

1. Find the general term formula for the sequence ${a_n}$.
2. Let $b_n=3a_{2n}+2n-7$, and $S_n$ is the sum of the first $n$ terms of the sequence ${b_n}$. Find $S_n$ and the minimum value of $S_n$.

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