
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
Suppose that in a right triangle $DEF$, with the right angle at $D$, the length of $DE$ is 8 units and the hypotenuse $EF$ is 17 units. A circle is inscribed such that it is tangent to $DF$, $EF$, and $DE$ at points $G$, $H$, and $I$, respectively. If $J$ is the point where the circle touches side $EF$, what is the length of segment $FJ$?

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