
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
The company consists of three boys and three girls. Each boy loves one of the three girls and each girl loves one of the boys; however, one of the girls noted sadly that in their company, nobody is loved by the one they love. How improbable is this sad circumstance if we assume that both boys and girls choose their affection more or less randomly?

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