
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 an experiment, the Wang Bo study group measured the length $y$ (in cm) of a spring hanging an object with the mass $x$ (in kg) as follows:

| Mass of Hanging Object $x$/kg | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ | $\ldots$ |
|-------------------------------|-----|-----|-----|-----|-----|-----|---------|
| Length of Spring $y$/cm       | $18$| $20$| $22$| $24$| $26$| $28$| $\ldots$ |

$(1)$ When the weight of the hanging object is $4$ kg, what is the length of the spring?
$(2)$ How does the dependent variable $y$ change as the independent variable $x$ increases?
$(3)$ Write down the relationship between the length of the spring $y$ and the mass of the hanging object $x$.
$(4)$ Find the length of the spring when hanging a $12$ kg object.

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