
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
In September every year, the third public holiday is National Science Popularization Day. In order to welcome the National Science Popularization Day in 2019, a school organized a science knowledge quiz competition, requiring each contestant to choose 3 out of 4 "ecological environmental protection questions" and 2 out of 2 "smart life questions" to answer (the probability of selecting each question is equal). Let the random variable $\xi$ represent the number of "smart life questions" selected by a contestant out of the 3 chosen questions.  
$(Ⅰ)$ Find the probability that the contestant selects exactly one "smart life question";  
$(Ⅱ)$ Find the distribution table and the mathematical expectation of the random variable $\xi$.

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