
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
A square $EFGH$ is inscribed in the region bound by the parabola $y = x^2 - 6x + 8$ and the $x$-axis. The vertex of the parabola is on one vertex of the square. Find the area of square $EFGH$.

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