
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 $\triangle ABC$ with side lengths $a$, $b$, and $c$.<br/>$(1)$ If $a=4$, $b=6$, and the perimeter of the triangle is less than $18$ and even. Find the length of side $c$;<br/>$(2)$ Simplify $|a+b-c|+|c-a-b|$.

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