
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 three-dimensional Cartesian coordinate system, the equation of the plane passing through $P(x_{0}, y_{0}, z_{0})$ with normal vector $\overrightarrow{m}=(a, b, c)$ is $a(x-x_{0})+b(y-y_{0})+c(z-z_{0})=0$, and the equation of the line passing through $P(x_{0}, y_{0}, z_{0})$ with direction vector $\overrightarrow{n}=(A, B, C)$ is $\frac{x-x_{0}}{A}=\frac{y-y_{0}}{B}=\frac{z-z_{0}}{C}$. Read the above information and solve the following problem: Given the equation of the plane $\alpha$ as $3x+y-z-5=0$, and the equation of the line $l$ passing through the point $P(0,0,0)$ as $x=\frac{y}{2}=-z$, then one direction vector of the line $l$ is ______, and the cosine value of the angle between the line $l$ and the plane $\alpha$ is ______.

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