
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
A certain agricultural trading company sells a batch of corn seeds. If the purchase quantity does not exceed $10$ kilograms, the price of the seeds is $20$ yuan per kilogram. If the purchase quantity exceeds $10$ kilograms, the price of the part exceeding $10$ kilograms is discounted by $20\%$. Let the purchase quantity be $x$ kilograms, and the payment amount be $y$ yuan.<br/>$(1)$ Find the analytical expression of $y$ in terms of $x$;<br/>$(2)$ A certain farmer purchases $30$ kilograms of corn seeds at one time, how much money does he need to pay?

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