
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 an isosceles triangle with a perimeter of $6$ cm, where the length of the base $y$ (in cm) is a function of the length of the legs $x$ (in cm).  
$(1)$ Write the functional relationship of $y$ in terms of $x$.  
$(2)$ Write the range of values for the independent variable $x$.

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