
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
Experience shows that in a certain growth stage, the larger the breast diameter (the diameter of the main trunk of the tree 1.3m above the ground), the taller the tree. Through measuring and studying a certain type of tree, it is found that the height $y$ (in meters) of this type of tree is a linear function of its breast diameter $x$ (in meters). It is known that when the breast diameter of this type of tree is $0.2m$, the height of the tree is $20m$; when the breast diameter is $0.28m$, the height is $22m$.  
$(1)$ Find the expression of the function between $y$ and $x$;  
$(2)$ When the breast diameter of this type of tree is $0.3m$, what is its height?

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