
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 rectangle ABCD has DC = 3 * CB and points E and F lie on segment AB such that ED and FD trisect angle ADC, find the ratio of the area of triangle DEF to the area of rectangle ABCD.

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