
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 an arithmetic sequence $\{a_n\}$ satisfying $a_4 - a_2 = 2$, and $a_1$, $a_3$, $a_7$ form a geometric sequence.
$(1)$ Find the general term formula for $\{a_n\}$;
$(2)$ Let $b_n= \frac {a_n}{a_{n-1}} + \frac {a_{n-1}}{a_n} - 2$, calculate the sum of the first $n$ terms $S_n$ of the sequence $\{b_n\}$.

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