
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 right triangle \( KLM \), a circle is constructed on the leg \( KM \) as the diameter, which intersects the hypotenuse \( KL \) at point \( G \). A tangent to the circle is drawn through point \( G \), intersecting the leg \( ML \) at point \( F \). Find the length of \( FL \), given that \( KG = 5 \) and \( LG = 4 \).

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