
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
Two non-zero vectors $\vec{a}$, $\vec{b}$ are perpendicular to each other. Given the following equations:

1. $\vec{a} \cdot \vec{b} = 0$
2. $\vec{a} + \vec{b} = \vec{a} - \vec{b}$
3. $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}|$
4. $|\vec{a}|^2 + |\vec{b}|^2 = (\vec{a} + \vec{b})^2$
5. $(\vec{a} + \vec{b}) \cdot (\vec{a} - \vec{b}) = 0$

Determine which of the above equations are correct. Write the number of each correct conclusion.

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