
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 three sides of $\triangle ABC$, and satisfy $a+b=3c-2$, $a-b=2c-6$.  
$(1)$ Find the range of values for $c$;  
$(2)$ If the perimeter of $\triangle ABC$ is $18$, find the value of $c$.

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