
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
Given the parabola \(y^2=2x\) and the point \(M(4,0)\), find the number of lines that pass through a point on the parabola, intersect the parabola at two points, and form a triangle with \(M\) and the points of intersection with a total area of 1.

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