
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
Right $\triangle DEF$ with sides $DE = 6$, $EF = 8$, and $DF = 10$.  Rectangle $GHIJ$ is inscribed in $\triangle DEF$ with $G$ and $H$ on $\overline{DF}$, $I$ on $\overline{DE}$, and $J$ on $\overline{EF}$. If one side of the rectangle ($GH$) is parallel to $DE$, find the dimensions of the rectangle $GHIJ$.

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