
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
Inside square $ABCD$, right triangle $ABE$ has $AB$ as the hypotenuse with $E$ on diagonal $AC$. Point $G$ is the intersection of diagonal $BD$ and line segment $AE$. If the side length of square $ABCD$ is 2 units, find the area of triangle $ABG$.

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