
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
Right $\triangle ABC$ has $AB=6$, $BC=8$, and $AC=10$. Square $XYZW$ is inscribed in $\triangle ABC$ with $X$ and $Z$ on $\overline{AC}$, $Y$ on $\overline{BC}$, and $W$ on $\overline{AB}$. What is the side length of the square?

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