
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
Let \( XYZ \) be an acute-angled triangle. Let \( s \) be the side length of the square which has two adjacent vertices on side \( YZ \), one vertex on side \( XY \), and one vertex on side \( XZ \). Let \( h \) be the distance from \( X \) to the side \( YZ \) and \( b \) be the distance from \( Y \) to \( Z \).

(a) If the vertices have coordinates \( X=(2,4), Y=(0,0) \), and \( Z=(4,0) \), find \( b, h \), and \( s \).

(b) Given the height \( h=3 \) and \( s=2 \), find the base \( b \).

(c) If the area of the square is 2017, determine the minimum area of triangle \( XYZ \).

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