
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 rectangle $HIJK$, side $HI$ measures $8$ units and side $IJ$ measures $4$ units. Points $M$ and $N$ are on side $JK$ such that segment $JM$ measures $2$ units and segment $NK$ measures $1$ unit. Lines $HM$ and $IN$ intersect at $O$. What is the area of triangle $HIO$?

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