
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
There were 76 people in two rooms. When 30 people left one room and 40 people left the other room, the number of people left in each room was equal. How many people were initially in each room? (Don't forget to explain your answer.)

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