
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 the rectangle \(ABCD\), it is known that \(AB = 2\) and \(AD < \sqrt{2}\). An ellipse \(K\) is drawn with \(AB\) as the major axis and the length of the minor axis equal to \(\sqrt{2}|AD|\). A point \(P\) on ellipse \(K\) is chosen, different from the endpoints of the major axis. Connect \(PC\) and \(PD\) which intersect \(AB\) at points \(M\) and \(L\), respectively. Find the value of \(AM^2 + LB^2\).

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