
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 grain production base actively expands the scale of grain production in order to implement the call for planting oilseed rape in the middle season between two seasons of rice in suitable areas. They plan to conduct oilseed rape trials on the farmland in Zone A and Zone B of the base. The farmland in Zone A is $10,000$ mu more than that in Zone B. $80\%$ of the farmland in Zone A and all the farmland in Zone B are suitable for trials, and the areas of suitable farmland in the two zones are exactly the same.  
$(1)$ Find out how many mu of farmland are in Zone A and Zone B, respectively.  
$(2)$ After planting oilseed rape on all the suitable farmland in Zone A and Zone B, in order to strengthen the pest control of oilseed rape, the base dispatched a batch of drones with the same performance to spray insecticides on the trial farmland. Due to the difference in terrain between the two zones, the number of drone sorties dispatched to Zone B is $1.2$ times that of Zone A (with the same spraying time per sortie). After completing the spraying task, it was found that each sortie of drones dispatched to Zone A sprayed $\frac{50}{3}$ mu more on average than those dispatched to Zone B. Find out how many mu each sortie of drones dispatched to Zone A sprayed on average.

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