
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 $a$, $b$, $c$ are the three side lengths of $\triangle ABC$.  
$(1)$ If $a$, $b$, $c$ satisfy $|a-b|+|b-c|=0$, determine the shape of $\triangle ABC$.  
$(2)$ Simplify: $|a+b-c|+|b-c-a|$.

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