
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
Let α and β be two non-coincident planes, and m and n be two non-coincident lines. Consider the following four propositions:
1. If m is perpendicular to n, m is perpendicular to α, and n is not contained in α, then n is parallel to α;
2. If m is perpendicular to n, m is parallel to α, and n is parallel to β, then α is perpendicular to β;
3. If α is perpendicular to β, the intersection of α and β is m, n is contained in α, and n is perpendicular to m, then n is perpendicular to β;
4. If n is contained in α, m is contained in β, α intersects β but they are not perpendicular, then n and m are definitely not perpendicular.

The sequence numbers of all true propositions are ______.

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