
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 high school Grade 12 Class 1 is holding a New Year celebration event. They have prepared 10 raffle tickets, with 2 tickets for the first prize, 3 tickets for the second prize, and the rest for the third prize.

(I) Calculate the probability of randomly drawing 2 tickets and both are first prize tickets.
(II) Calculate the probability of randomly drawing 3 tickets and having at most 1 first prize ticket.
(III) Let $\xi$ denote the number of second prize tickets obtained from randomly drawing 3 tickets. Calculate the mathematical expectation of $\xi$.

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