
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 middle school plans to enrich the students' campus life by making a one-time purchase of several footballs and basketballs from a sports store (the price of each football is the same, and the price of each basketball is the same). Buying 3 footballs and 1 basketball requires 230 yuan; purchasing 2 footballs and 3 basketballs costs a total of 340 yuan.  
(1) How much does it cost to buy one football and one basketball?  
(2) According to the actual situation of the school, it is necessary to purchase a total of 20 footballs and basketballs from the sports store at one time, requiring that the number of footballs purchased be less than the number of basketballs, and the total cost does not exceed 1400 yuan. What are the possible purchasing plans for this school, and explain the reasons.

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