
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
(I) Given that $(2x-1)^{10}=a\_0+a\_1(x-1)+a\_2(x-1)^2+...+a_{10}(x-1)^{10}$, where $a\_i \in R, i=1,2,...,10$.

(i) Find $(a\_0+a\_1+a\_2+...+a_{10})$;

(ii) Find $a\_7$.

(II) In May 2017, Beijing held the "Belt and Road" International Cooperation Summit Forum. The organizing committee assigned five volunteers A, B, C, D, and E to four different positions: translation, tour guide, etiquette, and driver. Each position had at least one person, and all five people were capable of performing these four positions.

(i) If each person was not allowed to hold multiple positions, how many different allocation schemes were there?

(ii) If A and B were called away to other places, and the remaining three people were required to hold two positions each, how many different allocation schemes were there?

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