
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
In the triangular prism \( S-ABC \), \( SA \perp \) plane \( ABC \), \( AB \perp BC \), point \( E \) is the midpoint of \( SC \), \( D \) is a point on \( AC \), and \( DE \perp SC \). Also, \( SA = AB \) and \( SB = BC \). Find the dihedral angle between the faces \( BDE \) and \( BDC \) using \( BD \) as the edge.

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