
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
Find the area of the triangle $\triangle MFO$, where point $M$ lies on the parabola $y^2=4\sqrt{2}x$, $F$ is the focus of the parabola, and $O$ is the origin of the coordinate system, given that the distance from point $M$ to the focus $F$ is $4\sqrt{2}$.

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