
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 trapezoid \(ABCD\), \(AB \parallel DC\). \(CE\) is the angle bisector of \(\angle BCD\) and \(CE \perp AD\) at \(E\). Given \(DE = 2AE\) and \(CE\) divides the trapezoid into two areas \(S_1\) and \(S_2\) with \(S_1 = 1\), find \(S_2\).

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