
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 an obtuse triangle \(ABC\), a point \(L\) is chosen on the side \(AB\), which is equal to 14, such that it is equidistant from the lines \(AC\) and \(BC\). On the segment \(AL\), there is a point \(K\) that is equidistant from the vertices \(A\) and \(B\). Find the sine of angle \(ACB\) if \(KL = 1\) and \(\angle CAB = 45^\circ\).

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