
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
If the average (arithmetic mean) age of a group consisting of teachers and engineers is 45, the average age of teachers is 40, and the average age of engineers is 55, determine the ratio of the number of teachers to the number of engineers.

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