
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 are $1$ female teacher and $2$ male teachers participating in a speech contest. There are $2$ topics to choose from. With each contestant randomly selecting one topic from the pool with replacement, calculate the probability that exactly one male and one female teacher choose the same topic.

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