
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 $(1-2x)^7=a_0+a_1x+a_2x^2+\ldots+a_7x^7$.

Find: 
1. $a_1+a_2+\ldots+a_7$;
2. $a_1+a_3+a_5+a_7$;
3. $|a_0|+|a_1|+|a_2|+\ldots+|a_7|$.

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