
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
Define a new operation: $a\otimes b=a(1-b)$, where the right side of the equation involves regular multiplication and subtraction operations. For example, $(-1)\otimes 1=(-1)\times (1-1)=0$.
1. Calculate: $(1+\sqrt{2})\otimes \sqrt{2}$.
2. Jiaqi says: if $a+b=0$, then $a\otimes a+b\otimes b=2ab$. Do you agree with his statement? Please explain your reasoning.

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