
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 $(\sqrt{2}-x)^{10}=a_0+a_1x+a_2x^2+\cdots+a_{10}x^{10}$, calculate the value of $(a_0+a_2+\cdots+a_{10})^2-(a_1+a_3+\cdots+a_9)^2$.

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