
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 and each tie priced at $40. 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