
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
The traditional Chinese mathematical masterpiece "Nine Chapters on the Mathematical Art" records: "There are 5 cows and 2 sheep, worth 19 taels of silver; 2 cows and 5 sheep, worth 16 taels of silver. How many taels of silver is each cow and each sheep worth?" Based on the translation above, the following two questions are proposed:
1. Find out how many taels of silver each cow and each sheep is worth.
2. If a merchant is prepared to spend 20 taels of silver to buy cows and sheep (requiring both cows and sheep, and all taels of silver must be used up), how many different ways can the merchant make the purchase? List all possibilities.

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