
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
There are 6 translators, among whom A, B are proficient in English, C, D, E are proficient in Korean, and F is proficient in both. Now, 3 people need to be selected from them, requiring 1 English translator and 2 Korean translators.
(I) Calculate the probability that F is selected;
(II) Among the selected 3 people, randomly appoint 2 people as captain and vice-captain. Calculate the probability that the English translator is not the captain.

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