
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 parallelogram $ABCD$, point $E$ is taken on the diagonal $AC$ such that the distance $AE$ is one third of $AC$, and point $F$ is taken on the side $AD$ such that the distance $AF$ is one fourth of $AD$. Find the area of parallelogram $ABCD$, given that the area of the quadrilateral $ABGE$, where $G$ is the intersection point of the line $FE$ with the side $BC$, is 8.

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