
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
In triangle \(ABC\), \(AC = 2\sqrt{3}\), \(AB = \sqrt{7}\), and \(BC = 1\). A point \(K\) is taken outside the triangle such that the segment \(KC\) intersects segment \(AB\) at a point different from \(B\), and the triangle with vertices \(K\), \(A\), and \(C\) is similar to the original triangle. Find the angle \(AKC\), given that the angle \(KAC\) is obtuse.

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