
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 that the sequence $\{a_n\}$ is an arithmetic sequence, $a_1=3$ and $(a_3-1)$ is the geometric mean of $(a_2-1)$ and $a_4$.  
$(1)$ Find $a_n$;  
$(2)$ If the sum of the first $n$ terms of the sequence $\{a_n\}$ is $S_n$, $b_n= \dfrac {a_n}{S_n-n}$, $T_n=-b_1+b_2+b_3+…+(-1)^nb_n$, find $T_n$.

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