
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 rhombus $ABCD$ forms the base of a quadrilateral pyramid, where $\angle BAD=60^\circ$. It is known that $SA = SC$, $SD = SB = AB$. Point $E$ is taken on the edge $DC$ such that the area of triangle $BSE$ is the smallest among the areas of 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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