
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 the triangle $A B C$ with an area of one unit, let $D$ and $E$ be the trisection points on side $A B$, and let $F$ be the midpoint of side $A C$. The line $F E$ intersects line $C B$ at $G$, and the line $F D$ intersects line $C B$ at $H$. Determine the area of triangle $F G H$.

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