
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 the direction vector of line $l_1$ is $\mathbf{a} = (2, 4, x)$, and the direction vector of line $l_2$ is $\mathbf{b} = (2, y, 2)$, if $|\mathbf{a}| = 6$, and $\mathbf{a} \perp \mathbf{b}$, calculate the value of $x + y$.

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