
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 \(\left(x^{2}+2x-2\right)^{6}=a_{0}+a_{1}(x+2)+a_{2}(x+2)^{2}+\cdots+a_{12}(x+2)^{12}\), where \(a_{i}\) (\(i=1, 2, \cdots, 12\)) are real constants. Then \(a_{0}+a_{1}+2a_{2}+3a_{3}+\cdots+12a_{12} = \qquad \).

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