
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 plans:
Plan 1: Buy a suit and get a tie for free;
Plan 2: Pay 90% of the list price for both the suit and the tie.
(1) If a customer buys 20 suits and 22 ties, how much would they need to pay under Plan 1? And under Plan 2?
(2) If a customer buys 20 suits and x ties (x > 20), how much would they need to pay under Plan 1? And under Plan 2? (Express your answer in an algebraic expression involving x)
(3) If x = 30 in (2), calculate which plan would be more cost-effective using the algebraic expressions you derived?

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