
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 sports goods store sells badminton rackets and shuttlecocks of a certain brand. A pair of badminton rackets is priced at $100, and a box of shuttlecocks is priced at $20. Now, a school wants to buy 10 pairs of badminton rackets and $x$ boxes of shuttlecocks from the store, where $x > 10$. The store offers two discount options to the school.<br/>Option 1: Buy one pair of badminton rackets and get one box of shuttlecocks for free.<br/>Option 2: Pay 90% of the original price for both the badminton rackets and shuttlecocks.<br/>$(1)$ Express the amounts to be paid for both options in terms of $x$. Option 1: ______ dollars, Option 2: ______ dollars.<br/>$(2)$ When $x=60$, calculate and determine whether it is more cost-effective for the school to choose Option 1 or Option 2.

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