
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 the direction vector of the line $l$ be $\overrightarrow{m}=(2,-1,z)$, and a normal vector of the plane $\alpha$ be $\overrightarrow{n}=(4,-2,-2)$. If the line $l$ is perpendicular to the plane $\alpha$, then the value of the real number $z$ is ______.

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