
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 faces of a regular hexagonal pyramid form a $45^{\circ}$ angle with the plane of the base. We attach a plane $S$ to one edge of the base such that it intersects the faces associated with the edges adjacent to that edge in parallel segments. What angle does the plane $S$ make with the base?

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