
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
To implement the concept of "comprehensive development of morality, intelligence, physical fitness, aesthetics, and labor skills" and beautify the environment, the school organized students to plant two types of seedlings, A and B, around the campus during Labor Week. It is known that purchasing 3 seedlings of type A and 2 seedlings of type B costs 12 yuan; purchasing 1 seedling of type A and 3 seedlings of type B costs 11 yuan.  
$(1)$ Find the price of each seedling of type A and B.  
$(2)$ In this activity, a total of 200 seedlings of type A and B were planted. Assuming that the planted seedlings will grow into tall trees after several years, and the average value of each tree (including ecological and economic value) is 100 times the original price of the seedling. To obtain a value of no less than 50,000 yuan, how many seedlings of type B should be planted at least?

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