
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 certain tea shop in Tai'an sells Taishan Maiden Tea. The first purchase included 30 boxes of type A tea and 20 boxes of type B tea, totaling 6000 yuan. For the second purchase, the price per box for both types of tea increased by 20%. The shop then bought 20 boxes of type A tea and 15 boxes of type B tea, spending 5100 yuan. Find the price per box of type A and type B tea for the first purchase.

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