
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
On the side \(AD\) of the square \(ABCD\), a point \(K\) is marked, and on the extension of the ray \(AB\) beyond point \(B\), a point \(L\) is marked. It is known that \(\angle LKC = 45^\circ\), \(AK = 1\), and \(KD = 2\). Find \(LB\).

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