
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
$$
(\sqrt{2017} x-\sqrt{2027})^{2017} = a_{1} x^{2017}+a_{2} x^{2016}+\cdots+a_{2017} x+a_{2018}.
$$

Then, evaluate $\left(a_{1}+a_{3}+\cdots+a_{2017}\right)^{2} - \left(a_{2}+a_{4}+\cdots+a_{2018}\right)^{2}$.

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