
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 $L$ be the intersection point of the diagonals $CE$ and $DF$ of a regular hexagon $ABCDEF$ with side length 2. Point $K$ is defined such that $\overrightarrow{LK} = \overrightarrow{AC} - 3 \overrightarrow{BC}$. Determine whether point $K$ lies inside, on the boundary, or outside of $ABCDEF$, and find the length of the segment $KB$.

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