
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
In a rectangle, the lengths of two adjacent sides are $x$ cm and $4$ cm, and the perimeter of the rectangle is $y$ cm.  
$(1)$ Write the relationship between $y$ and $x$.  
$(2)$ Find the perimeter of the rectangle when $x=10$ cm.  
$(3)$ Find the value of $x$ when the perimeter of the rectangle is $30$ cm.

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