
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 clothing factory produces suits and ties, with each suit priced at $200$ yuan and each tie priced at $40$ yuan. During a promotional event, the factory offers customers two discount options:

1. Buy a suit and get a tie for free;
2. Pay $90\%$ of the list price for both suits and ties.

Now, a customer wants to buy $20$ suits and $x$ ties from the factory $(x > 20)$.

(1) If the customer chooses option 1 to purchase, the payment required is __________ yuan (expressed as an algebraic expression containing $x$); if the customer chooses option 2 to purchase, the payment required is __________ yuan (expressed as an algebraic expression containing $x$);

(2) If $x=30$, calculate which option is more cost-effective for the customer?

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