
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
Let $O$ be the origin. Determine a scalar $m$ such that for any points $E, F, G, H,$ and $I$ satisfying
\[4 \overrightarrow{OE} - 3 \overrightarrow{OF} + 6 \overrightarrow{OG} + m \overrightarrow{OH} - 2 \overrightarrow{OI} = \mathbf{0},\]
the five points $E, F, G, H,$ and $I$ are coplanar.

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