
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
Given that $\triangle ABC$ contains four levels of nested triangles, each with an area twice that of the next level inside it, starting from the smallest triangle at the deepest nested level with an area of 1, find the area of trapezoid $DBCE$, where $D$, $B$, $C$, $E$ are points on $\triangle ABC$, and $\triangle ADE$ includes the third level of nested triangles.

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