
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
Given a parallelepiped $ABCD-A_1B_1C_1D_1$, let point $E$ be any point inside the top face $A_1B_1C_1D_1$ (including the boundary). If $\overrightarrow{AE} = x\overrightarrow{AA_1} + y\overrightarrow{AB} + z\overrightarrow{AD}$, determine the relationship among $x$, $y$, and $z$ that must be satisfied.

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