
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
A caretaker is giving candy to his two babies. Every minute, he gives a candy to one of his two babies at random. The five possible moods for the babies to be in, from saddest to happiest, are "upset," "sad," "okay," "happy," and "delighted." A baby gets happier by one mood when they get a candy and gets sadder by one mood when the other baby gets one. Both babies start at the "okay" state, and a baby will start crying if they don't get a candy when they're already "upset".
    The probability that 10 minutes pass without either baby crying can be expressed as  $\frac{p}{q}$ . Compute  $p+q$ .

*2022 CCA Math Bonanza Team Round #7*

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