
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

Every Sunday, a married couple has breakfast with their mothers. Unfortunately, the relationships each spouse has with the other's mother are quite strained: both know that there is a two-thirds chance of getting into an argument with the mother-in-law. In the event of a conflict, the other spouse sides with their own mother (and thus argues with their partner) about half of the time; just as often, they defend their partner and argue with their own mother.

Assuming that each spouse's arguments with the mother-in-law are independent of each other, what is the proportion of Sundays where there are no arguments between the spouses?

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