
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 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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