
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 distinct planes. Consider the following propositions:

1. If two intersecting lines within plane α are parallel to two lines within plane β respectively, then plane α is parallel to plane β.
2. If a line l outside of plane α is parallel to a line within plane α, then line l and plane α are parallel.
3. If planes α and β intersect along line l, and if there is a line within plane α that is perpendicular to l, then planes α and β are perpendicular to each other.
4. The necessary and sufficient condition for line l to be perpendicular to plane α is for line l to be perpendicular to two lines within plane α.

Among the propositions above, the sequence numbers of true propositions are ______ (write down the sequence numbers of all true propositions).

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