
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 base of a quadrangular pyramid is a rhombus \(ABCD\) in which \(\angle BAD = 60^\circ\). It is known that \(SD = SB\) and \(SA = SC = AB\). Point \(E\) is taken on edge \(DC\) such that the area of triangle \(BSE\) is the smallest among all sections of the pyramid containing segment \(BS\) and intersecting segment \(DC\). Find the ratio \(DE : EC\).

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