
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
Let the arithmetic sequence $\{a_n\}$ have a common difference $d$, and the sum of the first $n$ terms be $S_n$. Let the geometric sequence $\{b_n\}$ have a common ratio $q$. Given that $b_1=a_1$, $b_2=2$, $q=d$, and $S_{10}=100$.
$(1)$ Find the general formula for the sequences $\{a_n\}$ and $\{b_n\}$.
$(2)$ When $d > 1$, let $c_n= \frac {a_n}{b_n}$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, denoted as $T_n$.

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