
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 $a \diamond b = a^2 - 2b$.

(1) Find the value of $(-1) \diamond 2$;  
(2) Does this new operation satisfy the commutative law? If not, please provide a counterexample; if it does, please explain why.

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