
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
Given a parallelogram \(KLMN\) with \(KL=8\), \(KN=3\sqrt{2}+\sqrt{6}\), and \(\angle LKN=45^{\circ}\). 

On side \(KL\), a point \(A\) is chosen such that \(KA:AL=3:1\). Through point \(A\), a line parallel to \(LM\) is drawn, and a point \(B\) is chosen on this line within the parallelogram. A point \(C\) is chosen on side \(KN\) such that \(KC=AB\). 

Lines \(LC\) and \(MB\) intersect at point \(D\). 

Find the angle \(\angle LAD\).

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