
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
If ${({1-4x})^{10}}={a_0}+{a_1}x+{a_2}{x^2}+⋯+{a_{10}}{x^{10}}$, then $\frac{{{a_1}}}{2}+\frac{{{a_2}}}{{{2^2}}}+⋯+\frac{{{a_{10}}}}{{{2^{10}}}}=$____.

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