
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 triangles ABC and DEF, angle BAC is 30 degrees and angle EDF is 30 degrees, respectively, with side AB = 4 units, AC = 5 units, and DE = 2 units, and the area of triangle ABC being known to be twice the area of triangle DEF, find the length of side DF.

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