
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 vectors $a = (m, n)$ and $b = (p, q)$, define $a \otimes b = mn - pq$. Consider the following four statements:
1. $a \otimes a = 0$;
2. $a \otimes b = b \otimes a$;
3. $(a + b) \otimes a = a \otimes a + b \otimes a$;
4. $(a \otimes b)^2 + (a \cdot b)^2 = (m^2 + q^2) \cdot (n^2 + p^2)$.

Identify the correct statements. (Write down the numbers of all correct statements.)

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