
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
The acute or right angle formed by two intersecting lines is called the "angle" between the two lines. Now, on a plane, there are several lines, each intersecting the others, and the "angle" between any two lines can only be $30^{\circ}, 60^{\circ}$, or $90^{\circ}$. What is the maximum number of lines?

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