
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 points \( A(1, 3), B(5, 4), C(3, 7), D(7, 1), E(10, 2), F(8, 6) \). If line \( l \) is parallel to line \( DF \), and the shortest distance from line \( l \) to any point inside (including the boundary) of triangle \( ABC \) is equal to the shortest distance from line \( l \) to any point inside (including the boundary) of triangle \( DEF \), find the equation of line \( l \).

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