
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  $\mathcal{P}$  be a parallelepiped with side lengths  $x$ ,  $y$ , and  $z$ .  Suppose that the four space diagonals of  $\mathcal{P}$  have lengths  $15$ ,  $17$ ,  $21$ , and  $23$ .  Compute  $x^2+y^2+z^2$ .

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