
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 α and β as two non-coincident planes, and m and n as two non-coincident lines, the following four statements are provided:
1. If line m is contained in plane α, line n is contained in plane α, line m is parallel to plane β, and line n is parallel to plane β, then plane α is parallel to plane β.
2. If line n is contained in plane α, line m is contained in plane β, plane α intersects plane β but is not perpendicular, then line n is not perpendicular to line m.
3. If plane α is perpendicular to plane β, the intersection of planes α and β is line m, and line m is perpendicular to line n, then line n is perpendicular to plane β.
4. If line m is parallel to line n, line n is perpendicular to plane α, and plane α is parallel to plane β, then line m is perpendicular to plane β. Among these statements, the numbers of all true propositions are __.

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