
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 square \( ABCD \) with side length \( 1 \), \( E \) is the midpoint of \( AB \) and \( F \) is the midpoint of \( BC \). The line segment \( EC \) intersects \( AF \) and \( DF \) at \( G \) and \( H \), respectively. Find the area of quadrilateral \( AGHD \).

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