
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
If the direction vectors of the line $x+3y-7=0$ and the line $kx-y-2=0$ are $\overrightarrow{i}$ and $\overrightarrow{j}$, respectively, then when $\overrightarrow{i} \cdot \overrightarrow{j} = 0$, the value of the real number $k$ is ______.

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