
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
In triangle $\triangle ABC$, angles $A$, $B$, and $C$ form an arithmetic sequence, and the sides opposite these angles are $a$, $b$, and $c$, respectively.  
$(1)$ If $\frac{a}{b}=\frac{{a+b}}{{a+b+c}}$, determine the shape of $\triangle ABC$.  
$(2)$ If $\triangle ABC$ is not an obtuse triangle, find the range of $\frac{a}{c}$.

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