
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 the following four propositions:
1. There are infinitely many lines that can be drawn through a point outside a plane at an angle $\theta$ to the plane;
2. If a line is parallel to two intersecting planes, then it must also be parallel to their line of intersection;
3. For two given skew lines, there is exactly one plane through any point in space that is parallel to both of these skew lines;
4. For two skew lines, there are infinitely many planes that form the same angle with these two skew lines.

The correct propositions are     . (Please fill in the numbers of all correct propositions)

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