
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, Xiaoming fixed the upper end of a spring and hung an object at its lower end. The table below shows several corresponding values of the length $y$ of the spring and the mass $x$ of the hanging object:

| Mass of Hanging Object $x$ (kg) | $0$ | $1$ | $2$ | $3$ | $4$ |
|---------------------------------|-----|-----|-----|-----|-----|
| Length of Spring $y$ (cm)       | $16$| $18$| $20$| $22$| $24$|

$(1)$ The table reflects the relationship between ______ and ______; ______ is the independent variable, and ______ is the dependent variable.  
$(2)$ The relationship between the length of the spring $y$ (in cm) and the mass of the hanging object $x$ (in kg) is ______.  
$(3)$ If the length of the spring is $27$ cm, what is the mass of the hanging object at this time (within the allowable range of the spring)?

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