
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 department store sells suits and ties, with each suit priced at $500 and each tie priced at $100. During the "National Day" period, the store decided to launch a promotion offering two discount options to customers. Now, a customer wants to buy 20 suits and $x$ ties ($x > 20$).

Option 1: Buy one suit and get one tie for free;
Option 2: Pay 90% of the total price for both the suit and tie at the regular price.

(1) If the customer chooses Option 1, the amount to be paid is _______ yuan;
If the customer chooses Option 2, the amount to be paid is _______ yuan;
(2) If $x = 30$, please explain through calculations which option is more cost-effective at this time?
(3) When $x = 30$, can you come up with a more cost-effective purchasing plan? Write down your purchasing plan and calculate how much money is needed for this plan.

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