
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 \\({{(3-2\sqrt{2}x)}^{50}}={{a}_0}+{{a}_1}x+{{a}_2}{{x}^{2}}+\ldots +{{a}_{50}}{{x}^{50}}\\), where \\({{a}_0},{{a}_1},{{a}_2},\ldots ,{{a}_{50}}\\) are constants, then \\({({{a}_0}+{{a}_2}+\ldots +{{a}_{50}})^2}-{{({{a}_1}+{{a}_3}+\ldots +{{a}_{49}})^2}}=\\)______．

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