
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
Two strawberry picking gardens, A and B, have the same quality of strawberries, and the selling price is $50$ yuan per kilogram. Both gardens have introduced a "weekend" discount plan. Garden A's discount plan is: visitors need to buy a $100$ yuan ticket to enter the garden, and they will receive a 40% discount on the picked strawberries. Garden B's discount plan is: visitors do not need to buy a ticket to enter the garden, and they will receive a 50% discount on the portion of strawberries picked over 6 kilograms. During the discount period, suppose a visitor picks $x$ kilograms of strawberries $(x > 6)$, the total cost at garden A is $y_{1}$ yuan, and the total cost at garden B is $y_{2}$ yuan. <br/>$(1)$ Find the functional relationship between $y_{1}$ and $y_{2}$ with respect to $x$; <br/>$(2)$ How should a visitor choose the garden to minimize the total cost? Explain the reason.

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