
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 square $ABCD$. Point $L$ is on the side $CD$ and point $K$ is on the extension of the side $DA$ beyond point $A$ such that $\angle KBL = 90^\circ$. Find the length of segment $LD$ if $KD = 19$ and $CL = 6$.

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