
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
Mrs. Li keeps chickens in two courtyards: east and west. It is known that there are 40 chickens in the east courtyard. Now she sells $\frac{1}{4}$ of the chickens in the west courtyard to a store, and $\frac{1}{3}$ of them to a factory. The sum of the remaining chickens equals $50\%$ of the total number of chickens originally in both the east and west courtyards. How many chickens were originally in both the east and west courtyards combined?

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