
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
The midpoint of side $BC$ of triangle $ABC$ is a vertex of a new triangle, whose other two vertices are determined by an intersecting line parallel to side $BC$ that intersects the sides $AB$ and $AC$ of the given triangle. What will be the position of the intersecting line if the area of the newly formed triangle takes on a minimum value?

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