
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 unit selects three people, A, B, and C, to form a team to participate in the "2010 Shanghai World Expo Knowledge Contest". When A, B, and C answer a question at the same time, it is known that the probability of A answering correctly is $\frac{3}{4}$, the probability of both A and C answering incorrectly is $\frac{1}{12}$, and the probability of both B and C answering correctly is $\frac{1}{4}$. It is stipulated that as long as one person in the team answers the question correctly, the team is considered to have answered the question correctly.
(Ⅰ) Find the probability of the team answering the question correctly;
(Ⅱ) In this competition, each team must answer 10 compulsory questions, with 20 points awarded for each correct answer, and 10 points deducted for each incorrect answer, in addition to not scoring for that question. If the probability of the team answering each question correctly is the same and the correctness of answering any question does not affect the answers to other questions, find the expected score of the team for the compulsory questions.

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