
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
Given that ${(2+x)}^{6}{(1−2x)}^{5}={a}\_{0}+{a}\_{1}x+{a}\_{2}{x}^{2}…+{a}\_{11}{x}^{11}$, find:

(1) ${a}\_{0}+{a}\_{1}+{a}\_{2}+…+{a}\_{11}$
(2) ${a}\_{1}+{a}\_{3}+{a}\_{5}+{a}\_{7}+{a}\_{9}+{a}\_{11}$
(3) $\dfrac{{a}\_{1}}{{2}^{1}}+ \dfrac{{a}\_{2}}{{2}^{2}}+ \dfrac{{a}\_{3}}{{2}^{3}}+…+ \dfrac{{a}\_{11}}{{2}^{11}}$

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