
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
\( AB \) is the common perpendicular segment of skew lines \( a \) and \( b \). \( A \) is on line \( a \) and \( B \) is on line \( b \). \( AB = 2 \), and the angle between the skew lines \( a \) and \( b \) is \( 30^\circ \). On line \( a \), \( AP = 4 \). What is the distance from point \( P \) to line \( b \)?

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