
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 propositions:
(1) Two parallel lines form equal angles with the same plane;
(2) Two lines that form equal angles with the same plane are parallel;
(3) A line forms equal angles with two parallel planes;
(4) A line forms equal angles with two planes, and these two planes are parallel.
Among these propositions, the correct ones are __________. (Fill in the numbers of all correct propositions)

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