
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
In a right triangle $XYZ$ with the right angle at $Y$, point $W$ is the foot of the altitude from $Y$ to side $XZ$. If $XW = 5$ and $WZ = 7$, calculate the area of $\triangle XYZ$ and the length of hypotenuse $XZ$.
A) Area = $6\sqrt{35}$, Hypotenuse = $12$
B) Area = $12\sqrt{35}$, Hypotenuse = $6$
C) Area = $7\sqrt{35}$, Hypotenuse = $12$
D) Area = $35\sqrt{6}$, Hypotenuse = $7$

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