
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
A line \( e \) is inclined at an angle of \( 40^\circ \) to a plane \( S \). The line \( e \) forms an angle of \( 49^\circ \) with a line \( f \) that passes through the foot of the perpendicular dropped from \( e \) to the plane \( S \). What is the angle between \( f \) and the projection of \( e \) onto the plane \( S \)?

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