
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
Two planes $\alpha$ and $\beta$ have normal vectors $\vec{u} = (3, -1, z)$ and $\vec{v} = (-2, -y, 1)$, respectively. If $\alpha \perp \beta$, then the value of $y + z$ is (    ).

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