
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 $a$, $b$, and $c$ are the lengths of the sides of $\triangle ABC$, and $a$, $b$, $c$ are all integers.  
$(1)$ Simplify: $|a-b+c|+|c-a-b|-|a+b|$;  
$(2)$ If $a^{2}+b^{2}-2a-8b+17=0$, find the perimeter of $\triangle ABC$.

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