
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 \\((x^{2}+1)(x-1)^{9}=a_{0}+a_{1}x+a_{2}x^{2}+\ldots+a_{11}x^{11}\\).
1. Find the value of \\(a_{2}\\).
2. Find the term with the largest coefficient in the expansion.
3. Calculate the value of \\((a_{1}+3a_{3}+\ldots+11a_{11})^{2}-(2a_{2}+4a_{4}+\ldots+10a_{10})^{2}\\).

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