
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 \(DF\) in a regular hexagon \(ABCDEF\) with side length 3. The point \(K\) is defined such that \(\overrightarrow{LK} = 3 \overrightarrow{AB} - \overrightarrow{AC}\). Determine whether point \(K\) lies inside, on the boundary, or outside of \(ABCDEF\), and find the length of the segment \(KC\).

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