
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, Xiao Liang fixed the upper end of a spring and hung an object at its lower end. The relationship between the length $y$ (in cm) of the spring and the mass $x$ (in kg) of the hanging object is shown in the table below:

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

$(1)$ The independent variable in the table is ______, and the dependent variable is ______;  
$(2)$ Write down the relationship between the length of the spring $y$ (in cm) and the mass of the hanging object $x$ (in kg) directly as ______;  
$(3)$ If the length of the spring is $32$ cm (within the spring's range), find the mass of the hanging object.

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