
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 $(1-2x)^{7}=a$_{0}+a$_{1}x+a$_{2}x^{2}+…+a$_{7}x^{7}$, find
$(
ef{I})a$_{0}+a$_{1}+…+a$_{7}
$(
ef{II})a$_{0}+a$_{2}+a$_{4}+a$_{6} and a$_{1}+a$_{3}+a$_{5}+a$_{7}
$(
ef{III}) the sum of all binomial coefficients.

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