
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 rectangle ABCD, AB=2, BC=4, and points E, F, and G are midpoints of BC, CD, and AD, respectively. Point H is the midpoint of GE. A diagonal AC intersects HF at point I. Calculate the area of the trapezoid formed by points F, G, I, H.

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