
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
Let \\({\left( \sqrt{2}-x\right)}^{10}={a}_{0}+{a}_{1}x+{a}_{2}{x}^{2}+\cdots+{a}_{10}{x}^{10} \\). Find the value of \\({\left({a}_{0}+{a}_{2}+\cdots+{a}_{10}\right)}^{2}-{\left({a}_{1}+{a}_{3}+\cdots+{a}_{9}\right)}^{2} \\).

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