
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 the vertices of the square $ABCD$ marked on a horizontal plane, there are trees. The height of the tree at $A$ is $7 \mathrm{~m}$, the tree at $B$ is $13 \mathrm{~m}$, and the tree at $C$ is $17 \mathrm{~m}$.

What is the minimum side length of the square if there is a point inside the square that is equidistant from the tops of all four trees? What is the height of the tree at vertex $D$?

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