
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
Among the following statements: 
1. Parallel vectors must be equal.
2. Vectors that are not equal must not be parallel.
3. Equal vectors must be collinear.
4. Collinear vectors must be equal.
5. Vectors with equal length are equal vectors.
6. Two vectors parallel to the same vector are collinear vectors. 
The correct proposition(s) is/are.

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