
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
Note: In order to help students better solve this question, we provide a solution approach. You can follow the instructions below to fill in the blanks to complete the answer. You can also choose other solution methods, in which case you do not need to fill in the blanks, just answer the question according to the general requirements. A tea shop deals with two types of tea, $A$ and $B$. In the first purchase, they bought 30 boxes of type $A$ tea and 20 boxes of type $B$ tea, spending a total of 7000 yuan. In the second purchase, the price of both types of tea increased by 20%. The shop bought 20 boxes of type $A$ tea and 15 boxes of type $B$ tea, spending a total of 6000 yuan. Find the price per box of type $A$ and type $B$ tea in the first purchase. Solution approach: Let the price per box of type $A$ tea in the first purchase be $x$ yuan, and the price per box of type $B$ tea be $y$ yuan. <br/>$(Ⅰ)$ According to the question, set up the equation system $\left\{\begin{array}{l}{0}\\{0}\end{array}\right.$<br/>$(Ⅱ)$ Solve this equation system to get $\left\{\begin{array}{l}{x=(\;)}\\{y=(\;)}\end{array}\right.$<br/>Answer: The price per box of type $A$ tea in the first purchase is ______ yuan, and the price per box of type $B$ tea is ______ yuan.

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