
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
Among the following propositions:  
(1) Two planes parallel to the same line are parallel; (2) Two planes parallel to the same plane are parallel;  
(3) Two lines perpendicular to the same line are parallel; (4) Two lines perpendicular to the same plane are parallel.  
The number of correct propositions is __________.

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