
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
Source: 2017 Canadian Open Math Challenge, Problem C3
-----
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 let  $b$  be the distance from  $Y$  to  $Z$ .

[asy]
pair S, D;
D = 1.27;
S = 2.55;
draw((2, 4)--(0, 0)--(7, 0)--cycle);
draw((1.27,0)--(1.27+2.55,0)--(1.27+2.55,2.55)--(1.27,2.55)--cycle);
label(" $X$ ",(2,4),N);
label(" $Y$ ",(0,0),W);
label(" $Z$ ",(7,0),E);
[/asy]

(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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