
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 that $\overrightarrow{a}$, $\overrightarrow{b}$, and $\overrightarrow{c}$ form a basis in space, and real numbers $x$, $y$, and $z$ satisfy $x\overrightarrow{a}+y\overrightarrow{b}+z\overrightarrow{c}= \overrightarrow{0}$, then the value of $x^2+y^2+z^2$ is _____________.

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